GIFT   OF 


7L 


RE  FOR 


TO  THE 


/ 
SMITHSONIAN  INSTITUTION, 


ON    THE 


HISTORY  OF  THE  DISCOVERY 


OF 


NEPTUNE. 


BY  BENJAMIN  APTHORP  GOULD,  JR. 


WASHINGTON    CITY: 

PUBLISHED  BY  THE  SMITHSONIAN  INSTITUTION. 
1850. 


REPORT 


ON   THE 


HISTORY    OF    THE    DISCOVERY 


NEPTUNE. 


BENJAMIN  APTHORP  GOULD,  JR. 


WASHINGTON    CITY: 

PUBLISHED  BY  THE   SMITHSONIAN   INSTITUTION. 
1850. 


CAMBRIDGE: 

STEREOTYPED   AND   PRINTED   BY 

METCALF     AND     COMPANY, 

PRINTERS  TO  THE  UNIVERSITY. 


REPORT. 


IN  a  general  account  of  the  discovery  of  the  planet  Nep- 
tune, and  of  the  remarkable  circumstances  which  preceded  and 
attended  this  discovery,  it  cannot  at  this  late  period  be  expected 
that  any  new  views  should  be  brought  forward,  or  any  material 
facts  cited,  which  have  escaped  the  notice  of  the  eminent 
astronomers  who  have  already  written  upon  this  subject.  The 
facts  are  before  the  world.  The  numerical  data  are  in  all  the 
books.  The  history  is  too  strange  to  be  forgotten  by  any  one 
who  has  once  studied  it.  In  the  following  Report,  therefore,  it 
can  scarcely  be  hoped  that  the  facts  should  be  more  clearly 
arranged  or  more  concisely  presented  than  has  already  been 
done  by  Airy,  Biot,  and  Herschel,  or  that  any  thing,  bearing  up- 
on the  history  prior  to  1847,  be  narrated,  which  cannot  be  found 
elsewhere.  ^ 

The  strange  series  of  wonderful  occurrences  of  which  I  am 
to  speak  is  utterly  unparalleled  in  the  whole  history  of  sci- 
ence ;  —  the  brilliant  analysis  which  was  the  direct  occasion  of 
the  search  for  a  trans-Uranian  planet,  —  the  actual  detection  of 
an  exterior  planet  in  almost  precisely  the  direction  indicated,  — 
the  immediate  and  most  unexpected  claim  to  an  equal  share  of 
merit  in  the  investigation,  made  in  behalf  of  a  mathematician 
till  then  unknown  to  the  scientific  world,  —  and  finally  the 
startling  discovery,  that,  in  spite  of  all  this,  the  orbit  of  the  new 
planet  was  totally  irreconcilable  with  those  computations  which 
had  led  immediately  to  its  detection,  and  that,  although  found 
in  the  direction  predicted,  it  was  by  no  means  in  the  predicted 


4  REPORT   ON   THE  HISTORY   OF 

place,  nor  yet  moving  in  the  predicted  orbit.  This  series  of 
events,  together  with  the  since  developed  theory  of  Neptune, 
constitute  the  subject  of  my  Report. 

The  correctness  of  the  prophecy,  made l  by  a  British  writer 
within  a  few  weeks  of  the  discovery  of  the  planet,  that  the 
future  historian  of  astronomy  would  find  it  necessary  to  change 
his  pen  more  than  once  while  discussing  this  subject,  will  hardly 
now  be  called  in  question  by  the  strongest  partisans  of  any  of 
those  illustrious  scientists,  who  have  occupied  themselves  with 
the  theories  of  Uranus  and  Neptune;  —  although  the  most 
important  point  at  issue  is  a  question  very  different  from  the  one 
then  anticipated. 

There  has  never  been  a  more  complicated  case  presented  for 
the  sober  judgment  of  the  impartial  historian ;  and  the  tempta- 
tions to  dwell  upon  the  romance  and  poetry  of  the  subject  are 
extremely  strong.  I  purpose,  however,  in  the  following  history 
of  the  circumstances  which  led  to,  and  have  been  connected 
with,  the  discovery  of  Neptune,  to  present  the  subject  as  simply 
as  possible  ;  leaving  to  others  the  philosophical  considerations  and 
poetic  fancies  which  it  suggests,  and  aiming  only  at  clearness 
and  impartiality.  I  shall  arrange  the  Report  as  nearly  as  possi- 
ble in  the  chronological  order. 

The  planet  Uranus  was  discovered  by  Sir  William  Herschel 
on  the  13th  of  March,  1781,  and,  although  at  first  supposed  to  be  a 
comet,  was  before  the  end  of  the  year  recognized  2  as  one  of  the 
primary  planets  of  our  solar  system.  Circular  elements  were 
first  computed3  during  the  summer  of  1781,  by  Lexell,  of  St.- 
Petersburg,  at  that  time  in  London  ;  and  others  were  soon  after 
published  in  Russia,4  France,5  and  Germany.6  The  computation 

1  London  Athenceum,  Nov.  21,  p.  1191. 

2  Memoires  de  I' Acad.  des  Sciences,  Paris,  1779,  p.  526  ;  Berliner  Astronomisches 
Jahrbuch,  1784,  p.  215. 

3  Ada  Acad.  Petrop.,  1780,  Mem.,  p.  307. 

4  Nova  Acta  Acad.  Petrop,,  I.,  Hist.,  pp.  72,  76,  81 ;  Acta  Acad.  Petrop.,  1780, 
Mem.,  p.  312. 

5  Lalande,  Mem.  Acad.  Sc.  Paris,  1779,  p.  526. 

6  KlOgel,  of  Helmstadt,  Berl.  Ast.  Jahrb.,  1785,  p.  193.    Hcnnnert,  ibid.,  p.  205. 


THE   DISCOVERY   OF  NEPTUNE.  5 

of  a  planetary  orbit  was  at  that  time  a  most  laborious  and  trou- 
blesome process,  by  no  means  to  be  compared  with  the  easy 
methods  in  use  since  Gauss  gave  l  to  the  world,,  ^he  elegant 
and  simple  formulas  of  the  "  Theoria  Motus"^  No  elliptic 
elements  were  computed,  therefore,  until  the  year  1783,  during 
which  year  elliptic  orbits  differing  but  slightly  from  each  other 
were  published  by  Mechain,2  Laplace,3  Caluso,4  and  Hennert ; 5 
and  in  the  French  and  German  astronomical  Ephemerides  for 
1787  (published  in  1784)  were  tables  of  the  new  planet.  The 
name  Uranus,  originally  proposed  6  by  Bode,  had  at  that  time 
become  almost  universal  upon  the  Continent,  although  in  Eng- 
land the  names  "  Herschel "  7  and  "  Georgium  Sidus  "  8  (or 
simply  "  The  Georgian  ")  were  generally  used  until  within  a 
very  few  years,  —  the  planet  being  still  designated  by  the  latter 
name  in  the  British  Nautical  Almanac.  The  symbol  adopted  9 
with  the  name  Uranus  was  that  of  platinum  (6),  but  in 
England  and  France  the  symbol  ¥ ,  formed  from  the  discov- 
erer's initial,  is  generally  used. 

In  the  mean  time  Bode,  the  Astronomer  Royal  of  Prussia, 
had  suggested 10  that  Uranus  might  have  been  observed  by  as- 
tronomers before  the  discovery  of  its  planetary  nature,  and 
consequently  that  earlier  observations  might  be  found  by  a 
proper  search  in  the  catalogues  of  fixed  stars.  This  happy  idea 
prompted  him  to  study  over  the  old  star-catalogues,  and  his 
search  was  crowned  with  abundant  success.11  In  August,  1781, 

1  March,  1809. 

2  Hist.  Acad.  Bed.,  1782,  pp.  41,  49. 

3  Mim.  de  Bruxelles,  T.  5,  Hist.,ip.  xlix.,  Mem.,  p.  43;  Journal  de  Paris,  May 
31,  1783 ;  Berl  Ast.  Jahrb.,  1786,  p.  247  ;  Conn,  des  Temps,  1786,  p.  3. 

4  Ephem.  Astron.  Medial,  1784,  p.  199. 

5  Berl.  Ast.  Jahrb.,  1786,  p.  223. 

6  Berl.  Gesellschaft  Naturforschender  Freunde,  March  12,  1782,  III.  p.  350. 

7  Proposed  by  Lalande,  Dec.  22,  1781;  v.  Mdm.  Acad.  Paris,  1779,  p.  526; 
Hist.  Acad.  Berlin,  1782,  p.  39. 

8  Proposed  by  Herschel,  Roy.  Soc.  Philos.  Trans.,  1783,  p.  1. 

9  Proposed  by   Koehler,  of  Dresden;  Berl.  Ast.  Jahrb.,  1785,  p.  191;  Nova 
Acta  Petrop.,  I.  69. 

10  Berl  Ast.  Jahrb.,  1784,  p.  218. 

11  See  also  Bode,  Vom  neuentdccJcten  Planeten,  Berl.,  1784. 


6  REPORT   ON   THE  HISTORY   OF 

he  discovered1  that  a  star2  (No.  964)  in  Tobias  Mayer's  Cata- 
logue, which  had  been  observed  3  September  25,  1756,  was  not 
to  be  found  in  the  place  indicated,  and  that  it  had  not  been 
mentioned  on  various  occasions  when  all  the  other  stars  of 
equal  magnitude  in  the  same  vicinity  had  been  observed. 
Uranus  must  have  been  nearly  in  that  place  at  the  same  time, 
according  to  the  orbits  of  Laplace  and  Mechain,4  and  the  pre- 
sumption became  thus  quite  strong,  that  this  supposed  fixed  star 
of  Mayer  was  really  the  planet  Uranus.  In  the  same  way 
Bode  and  Fixlmillner  of  Kremsmiinster  found,5  in  1784,  that 
a  star  observed6  by  Flamsteed,  December  |f,  1690,  and 
called  by  him  34  Tauri,  was  in  all  probability  also  Uranus. 
The  same  discovery  seems  to  have  been  made  and  verified7 
independently  in  France  by  Lemonnier  and  Montaigne.  Ob- 
servations of  the  planet  were  thus  obtained,  which  embraced 
an  interval  of  more  than  an  entire  revolution,  and  from  these 
two  old  observations  in  1690  and  1756,  and  the  two  oppositions 
of  1781  and  1783,  Fixlmillner  computed  elliptic  elements,8 
which  not  only  fully  satisfied  all  the  four  places  upon  which  they 
were  based,  but  all  the  observations  known.  They  were  as 
follows :  — 

Epoch,  Jan.  1st,  1784. 

o        /        //  days. 

Mean  anomaly,  297     9  25  Tropical  period,               30587.37 

Long,  perihelion,  167  31  33  Mean  distance,                 19.18254 

Long.  asc.  node,  72  50  50  Eccentricity,                  0.0461183 

Inclination,  0  46  20  Mean  daily  trop.  motion,  42".3704 

which,   as   the    event  has   proved,  were  very  near  the   truth. 


1  Berl.  Ast.  Jahrb.,  I784,p.  219  ;  1785, p.  189  ;  Wurm, Geschichte  des  Uranus,  p.  35. 

2  Reduced  Conn,  des  Temps,  1778,  p.  195;  Fixlmillner,  Berl.  Acad.,  1783,  Hist., 
p.  15  ;  Bessel,  Fundamenta  Astronomic,  p.  283. 

3  Mayer,  Opera  Inedita,  ed.  Lichtenberg,  I.  p.  72. 

4  Hist.  Acad.  Berl,  1782,  p.  40. 

5  Hist.  Acad.  Berl,  1783,  p.  15  ;  Berl  Astr.  Jahrb.,  1787,  pp.  243,  247. 

6  Hist.  Ccdestis  Britann.,  II.  p.  86,  2d  ed. 

7  Mem.  Acad.  Roy.  des  Sciences,  1784,  p.  353. 

8  Hist.  Acad.  Berl,  1783,  p.  19;  Berl.  Astr.  Jahrb.,  1787,  p.  249. 


THE  DISCOVERY   OF   NEPTUNE.  I 

Wurm,  of  Niirtingen,  computed,1  at  nearly  the  same  time,2 
elements  3  very  similar ;  and  Fixlmillner,4  von  Zach,5  and  others,6 
constructed  tables.  Those  by  the  former  are  in  the  Berlin  As- 
tronomical Almanac  for  1789  (published  1786).  These  tables, 
as  above  remarked,  satisfied  all  the  observations,  and  continued 
to  represent  the  planet's  course  most  satisfactorily  until  1788, 
when  a  discrepancy  between  theory  and  observation  became  very 
apparent ; 7  and  Fixlmillner  was  compelled  to  disregard  Flam- 
steed's  observation,  and  to  calculate  new  elements  and  tables 8 
from  the  oppositions  since  Herschel's  discovery,  and  the  single 
observation  by  Mayer.  But  at  a  later  period,  after  Gerstner,9 
Lalande,10  Oriani,11  and  Duval 12  had  determined  the  perturba- 
tions by  Saturn  and  Jupiter,  and  Delambre  had  published 13  his 
tables  of  Uranus,  the  discrepancies  vanished,  and  the  same  ele- 
ments were  made  to  represent  perfectly  all  the  modern  observa- 
tions, and  the  two  former  ones  of  Mayer  and  Flamsteed.  In  1788, 
Lemonnier  discovered  14  that  he  had  also  observed 15  Uranus  as  a 
fixed  star  in  1 764  and  1769.  These  observations  of  Uranus,  made 
prior  to  Herschel's  discovery  of  its  planetary  character,  are  called, 
by  way  of  distinction,  "  ancient  observations."  Others  have 
since  been  found,  so  that  we  now  have  twenty  in  all,  viz. :  — 

1  Geschichte  des  Planeten  Uranus,  p.  37 ;  Beti.  Astr.  Jahrb.^1788,  p.  193. 

2  Summer  of  1784. 

3  See  Reggio,  Ephem.  Astr.  Mediol,  1784,  p.  199. 

4  Berl  Astr.  Jahrb.,  1789,  p.  113. 

5  Ibid.,  1788,  p.  217. 

6  Caluso,  Him.  de   Turin,  1787,  pp.  113,  132,  137;  Dom  Nouet,  Conn,  des 
Temps,  1787,  p.  176;  Robison,  Trans.  R.  Soc.  Edinb.,  1788,  Vol.  I.  p.  305. 

7  Wurm,  Gesch.  des  Uranus,  p.  38. 

8  Berl  Astr.  Jahrb.,  1792,  p.  159. 

9  Ibid.,  1792,  pp.  214,  219. 

10  M&m.  de  VAcad.  Sc.  Paris,  1787,  p.  182. 

11  Ephem.  Astr.  Mediol,  1790,  1791. 

12  Him.  Acad.  Berl,  1789;  Berl.  Astr.  Jahrb.,  1793,  115. 

13  Computed  1789,  crowned  1790.    Wurm,  Geschichte  des  Uranus,  p.  89;  La- 
lande, Astronomic,  ed.  3me,  Vol.  I. 

14  See  Lalande,  Acad.  Sc.  Paris,  1789,  p.  204;  von  Zach,  Comm.  Soc.  Reg.  Got- 
ting.,  1789,  p.  91. 

15  Conn,  des  Temps,  1821,  p.  339. 


REPORT   ON   THE  HISTORY  OF 

One 1   in  1690,  by  Flamsteed,  Dec.  f  §. 

One2    «  1712,   «  Flamsteed,  *g^. 

Four  ^  «  1715,  «  Flamsteed,  j^ti^'"'  Apr.  ff. 

Two4    "  1750,  "  Lemonnier,  Oct.  14, Dec.  3. 

One  5     "  1753,  "  Bradley,  Dec.  3. 

One  6    "  1756,  "  Mayer,  Sept.  25. 

One  7    "  1764,  "  Lemonnier,  Jan.  15. 

Two8    "  1768,  "  Lemonnier,  Dec.  27,  30. 

Six  9     "  1769,  «  Lemonnier,  Jan.  15, 16, 20, 21, 22, 23. 

One 10   "  1771,  "  Lemonnier,  Dec.  18. 

Mr.  Le  Verrier  has,  however,  found  reason  n  to  suspect  the 
accuracy  of  Flamsteed's  observation  of  f^J,  1715,  so  that 
there  are  really  but  nineteen  available  ones. 

The  best  tables  of  Uranus  which  existed  before  the  masterly 
and  accurate  researches 12  of  Le  Yerrier,  in  1845  and  1846,  were 
those  13  computed  by  Bouvard  in  1821.  Bouvard  was  acquaint- 
ed with  all  the  ancient  observations  which  we  know,  excepting 
three  by  Flamsteed  in  1715.  In  the  introduction  to  his  tables, 
he  announced 14  that  he  had  been  utterly  unable  to  find  any  el- 
liptic orbit,  which,  combined  with  the  perturbations  by  Jupiter 
and  Saturn,  would  represent  both  the  ancient  and  the  modern 
observations.  The  best  tables  which  he  could  obtain  by  the 

Hist.  Ccel.  Brit.,  II.  86,  2d  ed. ;  Hist.  Acad.  Berl.,  1783,  p.  16. 
Hist.  Ccd.  Brit.,  IE.  p.  537. 

Ibid.,  pp.  549,  551 ;  Conn,  des  Temps,  1820,  pp.  409,  410. 
Conn,  des  Temps,  1821,  p.  339. 

Bradley,  Astron.  06s.,  I.  p.  155  ;  Bessel,  Fund.  Astr.,  p.  283 ;  Greenwich  Plan. 
Reduct.,  I.  p.  300. 

6  Hist.  Acad.  BerL,  1783,  p.  8  ;  Bessel,  Fund.  Astron.,  p.  284;  Conn,  des  Temps, 
1778,  p.  195. 

7  Bouvard,  Conn,  des  Temps,  1821,  pp.  341,  342. 

8  Ibid.,  pp.  341-343. 

9  Rid.,  pp.  341,343-347. 

10  Ibid,  pp.  341,  347. 

11  App.  Conn,  des  Temps,  1849,  p.  125. 

12  Comptes  Rendus  de  I1  Acad.  des  Sc.,  XXI.  p.  1050;  XXII.  p.  907. 

13  Tables  Astronomiques,  Paris,  1821. 


THE  DISCOVERY  OF  NEPTUNE.  9 

use  of  both  represented  neither  of  them,  in  any  way  at  all  sat- 
isfactory. On  the  other  hand,  by  using  modern  observations 
only,  he  was  enabled  to  find  elements  which,  although  they 
gave  errors  amounting  sometimes  to  74"  for  the  ancient  obser- 
vations, still  satisfied  all  the  modern  ones  comparatively  well,  — 
never  differing  more  than  10"  from  theory,  and  generally  much 
less. 

"  Such,"  said  he,1  "  is  the  alternative  which  the  formation  of 
tables  of  the  planet  Uranus  presents ;  —  if  we  combine  the  an- 
cient observations  with  the  modern  ones,  the  first  will  be  passa- 
bly represented,  while  the  second  will  not  be  represented  with 
the  precision  which  they  require  ;  —  but  if  we  reject  the  former, 
and  retain  the  latter  only,  the  resultant  tables  will  have  all  de- 
sirable precision 'for  the  modern  observations,  but  will  be  incapa- 
ble of  properly  satisfying  the  ancient  ones.  We  must  choose 
between  two  alternatives.  I  have  thought  it  proper  to  abide  by 
the  second,  as  being  that  which  combines  the  most  probabilities 
in  favor  of  the  truth,  and  I  leave  it  to  the  future  to  make  known 
whether  the  difficulty  of  reconciling  the  two  systems  result  from 
the  inaccuracy  of  the  ancient  observations,  or  whether  it  depend 
upon  some  extraneous  and  unknown  influence,  which  has  acted  on 
the  planet." 

He  therefore  summarily  rejected  the  former  observations,  and 
founded  his  tables  upon  the  latter  alone,  adducing  arguments 
against  the  accuracy  of  the  ancient  observations,  and  forgetting 
how  well  they  harmonized  with  one  another,  and  had  harmo- 
nized with  the  elements  obtained  soon  after  the  discovery  of  the 
planet. 

But  a  very  few  years  after  the  publication  of  Bouvard's  ta- 
bles, important  differences  between  theory  and  observation  be- 
came 2  again  manifest,  and  attracted  the  attention  of  astronomers. 

Airy  alluded,3  in  1832,  to  these  discrepancies,  in  his  Report 


2  See  Ast.  Nachr.,  IV.  p.  56;  VI.  pp.  195,  209  ;  KOnigsberg  Observ.,  1826  ;  Cam- 
bridge (Eng.)  Observ.j  1826,  1830. 

3  Reports  of  British  Association,  I.  p.  154. 

2 


10  REPORT   ON   THE  HISTORY   OP 

to  the  British  Association  on  the  Progress  of  Astronomy,  and 
mentioned  that  the  tables,  constructed  only  eleven  years  previ- 
ously, were  in  error  nearly  half  a  minute  of  arc. 

It  is  an  easy  thing  to  censure  Bouvard  for  the  readiness  with 
which  he  abandoned  the  ancient  observations,  —  now  that  we 
know  that  the  discrepancies  were  caused  by  the  action  of  an  ex- 
terior planet,  and  that  the  maximum  of  error  in  the  ancient  ob- 
servations amounted1  only  to  nine  seconds.  But  the  illus- 
trious Bessel,  who,  had  his  priceless  life  been  spared  a  very  little 
longer,  would  have  seen  his  suspicions  most  fully  confirmed, 
spoke  2  as  follows,  in  a  public  lecture,3  in  the  beginning  of  the 
year  1840,  six  years  and  a  half  before  the  discovery  of  Nep- 
tune :  — 

"  In  my  opinion,  Bouvard  made  much  too  light  of  the  matter ; 
inasmuch  as,  after  he  had  found  himself  unable  to  reconcile  the 
theory  both  with  the  ancient  observations  and  the  forty  years' 
series  of  modern  ones,  he  contented  himself  with  the  remark, 
that  the  former  were  not  so  accurate  as  the  latter.  I  have  my- 
self subjected  them  to  a  more  careful  investigation,  and  new  cal- 
culation, and  have  thereby  attained  the  full  conviction,  that  the 
existing  differences,  which,  in  some  cases,  exceed  a  whole  min- 
ute, are  by  no  means  to  be  attributed  to  the  observations." 

Bessel  had  already  4  pointed  out  one  error  in  Bouvard' s  ta- 
bles, in  the  equation  depending  on  the  mean  longitude  of  Saturn 
minus  twice  that  of  Uranus.  This  error  was  small  in  compari- 
son with  the  discordances  to  be  accounted  for,  —  but  we  thus 
see  how  early  he  was  engaged  upon  the  investigation. 

The  last  sentence  of  Bouvard's  introduction,  just  quoted, 
which  was,  in  fact,  the  first  published  suggestion  that  the  discord- 
ance between  the  theory  and  observations  of  Uranus  might  be 
due  to  the  influence  of  an  unknown  planet,  is  hardly  definite 
enough  to  be  viewed  historically  in  that  light.  But  the  follow- 

1  Proc.  Amer.  Acad.,  I.  p.  333. 

2  Bessel,  Populdre  Vorlesungen,  p.  448. 

3  In  Konigsberg,  Feb.  28th,  1840. 

4  Astron.  Nachrichten,  No.  48,  II.  p.  441. 


THE   DISCOVERY    OF   NEPTUNE.  11 

ing  extract  from  a  letter,1  written  November  17,  1834,  by 
the  Rev.  Dr.  T.  J.  Hussey,  of  Hayes,  to  Prof.  Airy,  —  now 
English  Astronomer  Royal  and  then  Director  of  the  Observa- 
tory of  Cambridge,  England,  —  although  first  published  2  since 
the  discovery  of  Neptune,  is  the  earliest  written  allusion  to  the 
subject  with  which  I  am  acquainted. 

"  The  apparently  inexplicable  discrepancies  between  the  an- 
cient and  modern  observations  suggested  to  me  the  possibility  of 
some  disturbing  body  beyond  Uranus,  not  taken  into  account, 

because  unknown Subsequently,  in  conversation  with 

Bouvard,  I  inquired  if  the  above  might  not  be  the  case :  his  an- 
swer was,  that,  as  might  have  been  expected,  it  had  occurred  to 
him,  and  some  correspondence  had  taken  place  between  Hansen 
and  himself  respecting  it.  Hansen's  opinion  was,  that  one  dis- 
turbing body  would  not  satisfy  the  phenomena  ;  but  that  he  con- 
jectured there  were  two  planets  beyond  Uranus.  Upon  my 
speaking  of  obtaining  the  places  empirically,  and  then  sweeping 
closely  for  the  bodies,  he  fully  acquiesced  in  the  propriety  of  it, 
intimating  that  the  previous  calculations  would  be  more  labori- 
ous than  difficult ;  that,  if  he  had  leisure,  he  would  undertake 
them  and  transmit  the  results  to  me,  as  the  basis  of  a  very  close 

and  accurate  sweep I  may  be  wrong,  but  I  am  disposed 

to  think,  that,  such  is  the  perfection  of  my  equatorial^  object- 
glass,  I  could  distinguish,  almost  at  once,  the  difference  of  light 

between  a  small  planet  and  a  star If  the  whole  matter 

do  not  appear  to  you  a  chimera,  which,  until  my  conversation 
with  Bouvard,  I  was  afraid  it  might,  I  shall  be  very  glad  of 
any  sort  of  hint  respecting  it." 

As  regards  the  opinion  attributed  in  this  letter  to  Prof.  Han- 
sen,  I  have  the  authority  *  of  that  eminent  astronomer  himself 

*  Prof.  Hansen  informs  me,  in  a  letter  received  since  this  account  was  written, 
that  Mr.  von  Lindenau  has  been  engaged  upon  a  history  of  the  discovery  of 
Neptune.  To  his  inquiries  upon  this  subject,  Prof.  Hansen  had  replied  in  the 
following  words,  which  he  has  also  authorized  me  to  make  public:  — 

"  Die  mich  betreffende  Aeusserung  in  Airy's  Aufeatze  ( Astr.  Nachr.,  No.  585, 

1  Notices  R.  Ast.  Soc.,  VII.  p.  123.  2  Nov.  13,  1846. 


12  REPORT   ON   THE  HISTORY   OF 

for  stating,  that  the  assertion  must  have  been  founded  on  some 
misapprehension,  as  he  is  confident  of  never  having  expressed  or 
entertained  that  belief. 

In  the  Notices  of  the  Royal  Astronomical  Society  for  Novem- 
ber 13th,  1846,  is  a  most  important  publication  l  by  the  Astron- 
omer Royal,  entitled,  "  An  Account  of  some  Circumstances  his- 
torically connected  with  the  Discovery  of  the  Planet  exterior  to 
Uranus. "  In  this  paper  is  a  series  of  extracts  from  letters,  be- 
fore unpublished,  which  furnish  the  testimony  to  a  great  part  of 
the  history  anterior  to  the  actual  discovery.  From  the  first  let- 
ter2 in  the  series,  the  preceding  quotation  was  made. 

Mr.  Eugene  Bouvard,  nephew  of  the  author  of  the  Tables, 
wrote  as  follows  3  on  the  6th  October,  1837,  from  Paris,  to  the 
Astronomer  Royal  of  England  :  —  "  My  uncle  has  given  me  the 
tables  of  Uranus  to  reconstruct.  In  consulting  the  comparisons 

s.  136,  und  R.  Ast.  /Sbc.,  VII.  p.  123)  1st  jedenfalls  unrichtig.  Ich  besitze  freilich 
keine  Copien  von  meinen  Briefen  an  Bouvard,  aber  ich  finde  in  seinen  Briefen 
an  mich,  die  ich  wieder  durchlas,  als  mir  Airy's  Aufsatz  bekannt  wurde,  keine 
Spur,  dass  ich  gegen  ihn  die  von  Hussey  mir  in  den  Mund  gelegte  Aeusserung 
gemacht  hatte.  Auch  war  dies  unmoglich,  da  ich  meine  darauf  beziiglichen  Ar- 
beiten  nicht  so  weit  fortgesetzt  habe,  urn  darUber  eine  bestimmte  Ansicht  habcn 
zu  konnen.  Ich  kann  moglicher  Weise  geschrieben  haben,  dass  vielleicht  die  bis 
dahin  in  der  Bewegung  des  Uranus  nicht  erklarten  Abweichungen  von  der  Theo- 
rie  nicht  von  einem,  sondern  von  mehreren  auf  ihn  einwirkenden.  unbekannten 
Planeten  herrtlhrten  ;  aber  dass  Ein  storender  Korper  die  Abweichung  nicht  er- 
klaren  konne,  habe  ich  auf  keinen  Fall  behauptet.  Airy,  dem  ich  kurz  nach  dem 
Erscheinen  seines  Aufsatzes  darOber  schrieb,  antwortete,  dass  er  in  seinem 
nachsten  Artikel  Ober  Neptun  davon  Gebrauch  machen  wollte.  Es  ware  mir 
lieb,  wenn  dieses  auch  in  dem  Ihrigen  geschahe.  Immer  ist  es  meine  feste 
Ansicht  gewesen,  dass  die  Anomalien  in  der  Bewegung  des  Uranus  nichts  andcrs 
sind,  als  die  Wirkung  eines  oder  mehrerer  oberhalb  befindlichen  Planeten,  und  ich 
befand  mich  daruber  in  Opposition  mit  Bessel  und  Nicolai,  welche  beide  dieses 
fur  unmoglich  hielten.  Ersterer  ist  indess  in  seinen  letzten  Lebensjahren  von 
dieser  Ansicht  abgegangen,  und  hat  sich  ernstlich  mit  der  Aufsuchung  dieses 
Planeten  durch  Rechnung  beschaftigt.  Ich  hatte  in  den  zwanziger  Jahren  angc- 
fangen  mich  mit  dieser  Aufgabe  zu  beschaftigen,  —  gab  die  Arbeit  aber  wicdcr 
auf,  und  habe  sie  seitdem  wegen  anderer  Untersuchungen  ganz  aus  dem  Ge- 
sicht  verloren.  Eine  Stelle,  wo  LeVerrier  sagt  dass  die  Uranusbcobachtungen  der 
letzten  20  Jahren  nothwendig  waren,  um  ein  sicheres  Eesultat  zu  erlangen,  lasst 
es  mich  nicht  bereuen,  damals  meine  Arbeit  liegen  gelasscn  zu  haben." 

1  Notices  R.  Astron.  Sbc.,  VII.  p.  121.       2  Ibid.,  p.  123.  3  Ibid.,  p.  125. 


THE  DISCOVERY  OF  NEPTUNE.  13 

which  you  have  made  between  observations  of  this  planet  and 
the  calculations  in  the  tables,  it  will  be  seen  that  the  differences 
in  latitude  are  very  large,  and  are  continually  becoming  larger. 
Does  this  indicate  an  unknown  perturbation  exercised  upon  the 
motions  of  this  star  by  a  body  situated  beyond  ?  *  I  do  not 
know,  but  this  is  at  least  my  uncle's  idea." 

Prof.  Airy  remarked  in  his  reply,1  that  the  error  in  latitude 
was  very  small ;  —  that  it  was  the  errors  in  the  longitude  which 
were  increasing  with  so  fearful  rapidity.  And,  a  few  months 
after,  he  showed 2  that  the  tabular  radius-vector  of  Uranus  was 
much  too  small.  This  result  of  observations  at  the  quadratures 
was  one  to  which  Prof.  Airy,  both  at  that  time  and  uniformly 
since,  attached  great  importance. 

It  is  from  this  period,  that  the  definite  belief  of  most  astrono- 
mers in  the  existence  of  a  trans-Uranian  planet  appears  to  date. 
Numerous  mathematicians  subsequently  conceived  the  purpose  of 
entering  earnestly  into  laborious  and  precise  calculations,  in 
order  to  decide  whether  the  assumption  of  an  exterior  cause  of 
disturbance  were  absolutely  necessary,  and,  if  so,  to  determine 
from  the  known  perturbations  their  unknown  cause.  The  Astron- 
omer Royal  most  justly  expresses  3  himself  "  confident,  that  it  will 
be  found  that  the  discovery  is  a  consequence  of  what  may  prop- 
erly be  called  a  movement  of  the  age ;  that  it  has  been  urged 
by  the  feeling  of  the  scientific  world  in  general,  and  has  been 
nearly  perfected  by  the  collateral,  but  independent,  labors  of  va- 
rious persons  possessing  the  talents  or  powers  best  suited  to  the 
different  parts  of  the  researches." 

The  problem  became,  from  this  time  forth,  one  of  the  most 
important  questions  of  Physical  Astronomy.  Astronomers  in 
various  countries  busied  themselves  with  it,  and  spoke  of  it 
without  reserve. 


=*  "  Cela  tient-il  a  une  perturbation  inconnue  apportee  dans  les  mouvements  de 
cet  astre  par  un  corps  situe  au-dela  ?  " 

1  Notices  R.  Astron.  Soc.,  VII.  p.  126.      3  Notices  R.  Astr.  Soc.,  VII.  p.  122. 

2  Astr.  Nachr.,  No.  349,  XV.  p.  217. 


14  REPORT   ON   THE  HISTORY   OF 

The  first  decided  opinion,  publicly  expressed,  was,  I  believe, 
that  of  Bessel,  in  the  lecture  l  delivered  at  Konigsberg  on  the 
28th  February,  1840  ;  from  which  I  have  already  quoted.  He 
had,  at  that  time,  already  repeated  the  calculations  of  the  elder 
Bouvard,  and  convinced  himself  that  the  ancient  and  modern 
observations  could  not  be  reconciled  by  any  modification  of  the 
elements  ;  and  that  the  differences  could  not  be  attributed  to 
inaccuracy  of  instruments,  or  to  methods  of  observation. 

"  From  all  these  investigations,"  said  he,2  "  I  have  arrived  at 
the  full  conviction,  that  we  have  in  Uranus  a  case  to  which  La- 
place's assertion  *  is  not  applicable  .....  We  have  here  to  do 
with  discordances,  whose  explanation  can  only  be  found  in  a  new 
physical  discovery  .....  Farther  attempts  to  explain  them 
must  be  based  upon  the  endeavor  to  discover  an  orbit  and  a 
mass  for  some  unknown  planet,  of  such  a  nature,  that  the  result- 
ing perturbations  of  Uranus  may  reconcile  the  present  want  of 
harmony  in  the  observations.  If  the  motions  of  Uranus  can 
actually  be  explained  in  this  way,  the  lapse  of  time  will  raise 
this  explanation  to  the  rank  of  evidence,  in  the  same  degree  in 
which  it  will  exhibit  the  influence  of  this  new  power.  And  this, 
too,  must  exert  influences  upon  the  motion  of  Saturn,  which  are 
indeed  smaller,  but  will,  nevertheless,  hardly  be  able  to  escape  a 
special  investigation,  and  will  thus  afford  an  independent  confir- 
mation of  the  existence  of  the  new  planet." 

In  continuing  his  lecture,  Bessel  dwelt  long  upon  the  labor 
and  difficulty  of  the  problem.  He  spoke  of  the  painful  amount 
of  preparatory  labor  to  be  performed,  alluded  3  to  the  patience 
and  care  with  which  his  young  friend  and  pupil,  Flemming,  had 
already  reduced  all  the  observations  of  Uranus,  and,  with  father- 
ly kindness,  he  encouraged  him  in  his  work. 

The  labors  of  the  talented  and  enthusiastic  Flemming  were 


*  i.  e.,  that  the  theory  of  gravitation  entirely  explained  all  motions  observed  in 
our  solar  system. 

1  Bessel,  Popul.  Vorles.,  p.  408.  3  Ibid.,  p.  452. 

2  /6eW.,pp.  449,  450. 


THE   DISCOVERY   OF   NEPTUNE.  15 

interrupted  by  his  early  death.  Eessel  himself  was  upon  the 
point  of  commencing  the  investigation  which  he  had  proposed, 
when  he  sank  beneath  the  weight  of  his  labors  ;  and  "  the  prize 
toward  which  he  had  stretched  forth  his  hand  was  wrested  from 
him " l  by  the  lingering  and  painful  disease  which  closed  the 
long  series  of  his  brilliant  investigations,  and  removed  him  from 
the  world. 

Sir  John  Herschel  stated  publicly,2  soon  after  the  discovery  of 
Neptune,  that  Bessel,  while  in  England,  in  1842,  conversed  with 
him  concerning  the  probability  that  the  motions  of  Uranus  were 
disturbed  by  an  exterior  planet,  and  later  in  the  same  year,  in  a 
letter  from  Konigsberg,  intimated  that  he  was  engaged  in  re- 
searches relative  to  these  perturbations.  Professor  Schumacher  3 
has  promised  to  publish  Flemming's  reduction  of  the  Uranus-ob- 
servations in  the  Astronomische  Nachrichten. 

Meantime  Mr.  Eugene  Bouvard,  in  Paris,  had  been  engaged 
upon  the  same  labors.  In  May,  1844,  he  wrote  again  4  to  Mr. 
Airy,  that  he  had  not  only  reduced  the  observations  of  Uranus 
anew,  but  that  he  had  reconstructed  tables,  and  succeeded  in 
satisfying  the  modern  observations  so  nearly  that  the  extreme  of 
discordance  amounted  only  to  fifteen  seconds,  while  the  tables  of 
his  uncle  gave  places  nearly  two  minutes  out  of  the  way. 

But  it  must  be  observed,  on  the  other  hand,  that  the  ancient 
observations  were  not  represented  with  any  degree  of  accuracy ; 
and,  as  regards  the  modern  ones,  fifteen  seconds,  although  but  a 
small  angle,  — a  single  second  of  time, — is  nevertheless  five  times 
the  amount  of  error  which  we  are  warranted  in  assuming.  5 

Thus  not  only  the  investigations  of  Bessel  previous  to  1840, 
but  the  entirely  independent  ones  of  Bouvard,  between  1837 
and  1844,  showed  the  impossibility  of  explaining  all  the  observ- 
ed motions  of  Uranus  by  known  causes.  The  Royal  Society  of 


Schumacher,  Introduction  to  Bessel's  Popular  Lectures,  p.  iv. 

Letter  to  London  Atlienwum,  Oct.  3,  1846. 

Introduction  to  Bessel's  Lectures,  p.  iv. 

Airy's  Account,  letter  No.  5,  Notices  Astr.  Soc.,  VII.  p.  127. 

Proceedings  Amer.  Acad.,  I.  p.  333. 


16  REPORT   ON   THE  HISTORY   OP 

Sciences  of  Gottingen  had  already  proposed,  as  a  prize-ques- 
tion,1 in  1842,  the  full  discussion  of  the  theory  of  the  motions 
of  Uranus,  with  special  reference  to  the  cause  of  the  large 
and  increasing  errors  of  Bouvard's  tables. 

The  death  of  Flemming  and  the  feebleness  and  illness  of 
Bessel  put  a  stop  to  their  researches  in  Germany;  and  from 
this  period  we  know  of  but  two  mathematicians,  Messrs.  Adams, 
of  Cambridge  University,  in  England,  and  Le  Verrier,  in  Paris, 
who  busied  themselves  with  the  problem.  Mr.  Adams  states 2 
that  his  attention  was  first  called  to  the  subject  by  reading,  in 
the  summer  of  1841,  Mr.  Airy's  Report  on  the  Progress  of  As- 
tronomy. Mr.  Le  Verrier  undertook 3  the  investigation  at  the 
request  of  Arago,  the  Director  of  the  Observatory  of  Paris. 
That  eminent  scientist  had  doubtless  been  impressed  by  the  com- 
putations of  Bouvard  with  the  necessity  of  the  research ;  and 
the  Astronomer  Royal  expresses 4  his  conviction,  that  the  knowl- 
edge of  Bouvard's  labors  "  tended  greatly  to  impress  upon  as- 
tronomers, both  French  and  English,  the  absolute  necessity  of 
seeking  some  external  cause  of  disturbance." 

Three  months  before  the  date  of  the  laskcited  letter  of  Bou- 
vard, Mr.  Adams  had  informed  Mr.  Airy,  through  Prof.  Challis, 
that  he  was  engaged  in  researches  of  a  precisely  similar  nature. 
The  letter5  of  Prof.  Challis  is  dated  February,  1844,  and  was 
written  to  obtain  the  reductions  of  the  Uranus-observations 
which  had  been  made  at  Greenwich.  Airy  immediately  6  for- 
warded the  complete  series  of  heliocentric  errors  of  the  Uranus- 
tables,  —  both  in  longitude  and  latitude,  —  for  all  the  Green- 
wich observations  from  1754  to  1830. 

During  the  summer  of  1845,  Mr.  Arago  represented,  as 
above  stated,  to  Mr.  Le  Verrier,  then  colleague  of  the  venerable 


1  Abhandl  d.  KOnigl.  Gesellschaft,  II.  p.  x. 

2  Adams's  "Explanation,"  p.  3,  Naut.  Aim.,  1851. 

3  Le  Verrier's  "  Recherches,"  p.  4,  Conn,  des  Temps,  1849. 

4  "Account"  Ast.  Soc.  Notices,  VII.  p.  127. 
8  "  Account,"  letter  No.  6,  p.  128. 

6  Ibid.,  letter  No.  7,  p.  128. 


THE  DISCOVERY   OF   NEPTUNE.  17 

and  illustrious  Biot,  the  transcendent  importance  of  the  ques- 
tion, and  urgently  pressed  him  to  enter  into  a  full  discussion  of 
the  subject.  Le  Verrier  did  this,  and  presented  his  first  paper  l 
to  the  Academy  of  Sciences  on  the  10th  November,  1845. 

A  fortnight  previous,  Mr.  Adams  had  communicated  2  to  Mr. 
Airy,  that,  according  to  his  calculations,  the  observed  inequalities 
of  Uranus  might  be  explained  by  supposing  an  exterior  planet 
with  a  mass  and  orbit  as  follows  :  — 
Mean  distance  (assumed  nearly  in  accord- 
ance with  Bode's  law),  .         .     f< ' '.'! Of     .         .  38.4 
Mean  sidereal  motion  in  365.25  days,       ...       1°  30'. 9 
Mean  longitude,  October  1st,  1845,     .         .         .        323°  34' 
Longitude  of  the  perihelion,  .         .         .         .         .  315°  55' 

Eccentricity, 0.1610 

Mass,  that  of  the  sun  being  unity,  .         .         .  0.0001656 

With  these  elements  Mr.  Adams  gave  a  table  of  remaining  er- 
rors of  longitude  for  every  three  years  of  the  modern  observa- 
tions, none  of  which  exceeded  two  and  a  quarter  seconds.  The 
ancient  observations  were  satisfied  within  12",  excepting  Flam- 
steed's  in  1690,  which  differed  by  44". 4,  not  having  been  used 
in  the  equations  of  condition.  It  was,  however,  probable,  he 
thought,  that  a  small  change  in  the  mean  motion  of  the  hypo- 
thetical planet  would  reduce  this  discordance  materially. 

Prof.  Airy,  in  replying,  desired3  to  know  whether  this  as- 
sumed perturbation  would  explain  the  error  of  the  radius-vector, 
as  he  considered  that  this  trial  would  be  an  experimentum  crucis. 
For  some  reason,  no  answer  was  received.  This  is  deeply  to  be 
regretted,  as,  had  an  affirmative  answer  been  given,  Airy  would 
undoubtedly  4  have  procured  the  publication  of  Mr.  Adams's  re- 
sults, and  the  painful  discussion  concerning  priority  would  have 
been  spared.  As  the  case  now  stands,  the  question  of  priority 
depends  upon  another  question,  —  whether  Adams's  communica- 
tion of  his  results  to  the  Astronomer  Royal  can  be  considered  as 
a  publication  of  them. 

1  Comptes  Rendus,  XXI.  p.  1050.  3  «  Account,"  letter  No.  12,  p.  130. 

2  Airy's  Account,  letter  No.  11,  p.  129.         4  Ibid.,  p.  131. 

3 


18  REPORT   ON   THE   HISTORY   OF 

The  next  letter  of  Mr.  Adams,  which  has  been  printed,1  is 
dated  September  2,  1846.  Le  Yerrier  had,  in  the  mean  time, 
not  only  published  2  the  memoir  already  alluded  to,  in  which  the 
perturbations  of  Uranus  by  Jupiter  and  Saturn  are  fully  devel- 
oped, calculated,  and  discussed,  —  but  had  communicated  to  the 
Academy  two  other  most  important  papers.  In  one,3  presented 
on  June  1st,  1846,  he  proved4  that  the  motions  of  Uranus  could 
not  be  accounted  for,  except  by  introducing  the  perturbative  in- 
fluence of  an  unknown  planet,  for  which  he  assigned  an  approx- 
imate place.  In  the  other,5  he  found  an  orbit,  a  mass,  and  a 
more  precise  position  for  the  disturbing  planet.  This  was  pre- 
sented on  the  31st  August. 

Mr.  Airy  mentions,6  that  on  the  29th  June,  at  a  meeting  of 
the  Board  of  Visitors  of  the  Greenwich  Observatory,  at  which 
Sir  John  Herschel  and  Prof.  Challis  were  present,  he  spoke  of 
the  extreme  probability  that  another  planet  would  be  discovered 
within  a  short  time ;  and  assigned,  as  a  reason  for  this  belief, 
the  coincidence  between  Mr.  Le  Yerrier' s  results  and  those  of 
Mr.  Adams.  He  had  addressed 7  a  letter  to  Mr.  Le  Yerrier, 
similar  to  that  sent  a  year  previously  to  Mr.  Adams,  to  make  in- 
quiries about  the  radius-vector.  Mr.  Le  Yerrier  answered  8  un- 
der date  of  June  28,  stating  that  the  errors  of  radius-vector 
must  be  accounted  for,  inasmuch  as  the  equations  of  condition 
depended  on  observations  at  the  quadratures  as  well  as  at  the 
oppositions.  Concerning  the  correctness  of  this  inference, 
however,  there  appears  room  for  discussion.  Le  Yerrier  called 
Airy's  attention  to  the  fact,  that  the  position  in  quadrature  in 
1844,  deduced  by  means  of  his  formulas  from  the  two  opposi- 
tions which  comprised  it,  only  differed  0".6  from  the  observed 
position,  which  proved,  he  said,  that  the  error  of  radius-vector 
had  entirely  disappeared.  This  he  considered  as  one  of  the 
strongest  arguments  in  favor  of  the  truth  of  his  results.  For, 

1  "  Account?  letter  No.  20,  p.  137.  5  Comptes  Rendus,  XXIII.  p.  428. 

2  Comptes  Rendus,  XXI.  p.  1050.  6  "Account,"  p.  133. 

3  Rid.,  XXII.  p.  907.  7  Letter  No.  13,  p.  132. 

4  Ibid.,  p.  911.  8  Letter  No   14,  p.  133. 


THE  DISCOVERY  OF  NEPTUNE.  19 

while  in  his  first  researches  he  only  made  use  of  oppositions, 
the  quadratures  were  represented  with  all  precision.  "  Le  ray- 
on vecteur,"  said l  he,  "  s'est  trouve  rectifie  de  lui-meme  sans 
que  Ton  1'eut  pris  en  consideration  d'une  maniere  directe.  Ex- 
cusez-moi,  Monsieur,  d'insister  sur  ce  point.  C'est  une  suite  du 
desir  que  j'ai  d'obtenir  votre  suffrage." 

At  Airy's  suggestion,2  Professor  Challis  had  already  com- 
menced3 a  search  for  the  planet  on  the  29th  July,  using  a  modi- 
fication of  a  plan  which  Mr.  Airy  had  drawn  up.  The  date  of 
the  letter  suggesting  this  search  was  July  9 ;  that  of  the 
general  plan  was  July  13.  Le  Verrier's  memoir,4  which  as- 
signed 325°  as  the  probable  longitude  of  the  planet,  was 
presented  to  the  French  Institute,  as  we  have  seen,  on  June  1st. 
Still,  it  does  not  appear  that  any  search  whatever  had  been 
instituted  in  the  intervening  time  in  any  part  of  Europe  or 
America ;  —  indeed,  there  is  no  account  of  any  search  having 
been  made  excepting  by  Professor  Challis,  before  the  night  of 
September  23. 

It  must,  indeed,  be  confessed  that  astronomers  in  general  did 
not  seem  to  consider  the  theoretical  results,  published  by  Mr. 
Le  Verrier,  as  necessarily  indicating  the  physical  existence  and 
true  position  of  such  an  exterior  planet.  Professor  Challis 
alone  —  the  only  astronomer  who  entered  into  a  systematic 
search  for  the  planet,  and  the  only  one  excepting  "Dr.  Galle,  the 
assistant  at  the  Royal  Observatory  of  Berlin,  whom  we  know  to 
have  even  looked  for  it  —  has  assigned,5  as  a  reason  which  de- 
terred him  from  an  earlier  search,  that  it  was  "  so  novel  a  thing 
to  undertake  observations  in  reliance  upon  merely  theoretical 
deductions ;  and  that,  while  much  labor  was  certain,  success 
appeared  very  doubtful."  But  is  there  any  practical  astrono- 
mer, in  a  latitude  permitting  the  search,  who  was  not  deterred 
by  the  same  considerations.  Even  in  Paris,  that  focus  of  sci- 
ence, with  its  many  and  powerful  telescopes,  with  its  numerous 

1  "  Account"  letter  No.  14,  p.  134.  4  Comptes  Rendus,  XXII.  p.  917. 

2  Ibid.,  pp.  135,  136.  6  Ast.  Soc.  Notices,  VII.  p.  145. 

3  Ast.  Soc.  Notices,  VII.  p.  145. 


20  REPORT   ON  THE   HISTORY   OF 

eminent  astronomers,  where  Mr.  Le  Verrier  was  known  and  his 
brilliant  genius  appreciated,  —  not  to  allude  to  the  American 
observatories,  furnished  with  some  of  the  finest  and  most  power- 
ful telescopes  which  have  left  the  ateliers  of  Munich,  —  we  have 
no  information  that  any  attempts*  were  made  to  test  the  physical 
accuracy  of  Le  Verrier's  results,  or  that  the  planet  was  even 
looked  for  on  one  single  evening. 

A  strange  contrast  to  this  apathy  on  the  part  of  other  astrono- 
mers is  furnished  by  the  demeanor  of  Le  Verrier  himself.  Hav- 
ing fairly  arrived  at  his  results,  he  looked  upon  them  as 
conclusive.  His  computations  had  been  an  earnest  work.  He 
had  employed  all  his  analytical  powers,  —  and  employed  them, 
too,  most  successfully,  —  to  refine  the  methods  which  he  used, 
and  to  narrow  the  field  of  his  inquiry;  all  his  powers  of 
application  and  numerical  research,  to  insure  precision;  —  and 
his  indomitable  perseverance,  in  carrying  out  his  computations 
with  full  vigor,  permitted  him  to  omit  no  possible  test  of  their 
accuracy.  He  proved  that  the  observations  of  Uranus  made  it 
necessary  to  assume  the  existence  of  some  unknown  disturbing 
body.-  For  the  observations  which  he  adopted  as  the  basis  of 
his  calculations,  he  had  assigned,  a  priori,  the  limits  of  error 
allowable ;  and  he  found  that  all  the  observations  could  be  satis- 
fied within  these  predetermined  limits  by  the  assumption  of  an 
exterior  planet,  moving  in  a  given  orbit,  and  having  a  given 
mass.  The  correctness  of  his  results  was  dependent  upon  no 
empirical  assumption.  He  gave  them,  therefore,  fearlessly  to  the 
world,  and  staked  his  reputation  upon  their  accuracy.  This 
forms  by  no  means  the  least  part  of  his  claims  to  the  respect  and 
admiration  of  scientists  throughout  the  world.  Had  the  planet 
not  been  found  in  the  predicted  place,  Le  Verrier  would  alone 
have  borne  the  mortification.  Neptune  was  discovered  in  almost 
precisely  the  direction  assigned,  and  Le  Verrier  receives  the 
admiration  so  justly  due  him. 


*  It  is,  perhaps,  due  to  the  Naval  Observatory  at  Washington,  to  make  some 
exception  in  its  favor.    Astr.  Nachr.,  XXVI.  p.  65. 


THE  DISCOVERY  OF   NEPTUNE.  21 

The  mass  and  orbit  given  in  the  memoir  of  August  31st  are  1 
as  follows  :  — 

Semiaxis  major,           ......  36.1539 

Sidereal  period,      ......  .  217^.387 

Eccentricity,       .......  0.10761 

Equation  of  the  center,  .....  7°  44'  44" 

Longitude  of  perihelion,  January  1,  1800,     .         .  284      5  48 

Mean  longitude,      ......  240    17  41 

Precession  in  47  years,         .         .     .  .  ...  -;     .         .  0    39  20 

Mean  sidereal  motion  in  47  years,    .       -.   f     .  77    50     3 

Mean  anomaly,  1847,  January  1,          ,,.,:;     .         .  34      1  56 

Mean  longitude,      .         .         .     ^  ,       .         .  318   47     4 
Mass,          .....         .r.     . 


The  geocentric  longitude,  resulting  from  this  orbit,  for  the  end 
of  September,  1846,  was  325°.  Le  Verrier,  in  acknowledging 
the  receipt  of  a  memoir,  made  use  of  the  opportunity  thus 
afforded,2  to  request  Dr.  Galle  to  look  for  the  planet.  The  letter 
reached  Berlin  3  on  the  23d  September,  and  Galle,  in  comply- 
ing with  this  request,  found,  on  the  same  evening,  a  new  planet 
in  longitude  325°  53',  or  within  55'  of  the  geocentric  place  4  as- 
signed by  Mr.  Le  Verrier. 

The  remembrance  of  the  enthusiasm  excited  by  this  discovery, 
of  the  amazement  with  which  the  tidings  were  received,  not  only 
by  astronomers,  but  by  almost  all  classes  of  the  community,  and 
of  the  homage  paid  to  the  genius  of  Le  Yerrier,  is  still  fresh  in 
the  memory  of  all.  Nations  vied  with  one  another  in  expres- 
sions of  their  admiration.5  Arago,  to  whom  the  right  of 
conferring  a  name  upon  the  new  planet  was  delegated  6  by  Le 
Verrier,  gave7  to  the  planet  the  name  of  that  geometer,  with 
the  symbol  !£,  deduced  from  the  initials  of  the  same.  This 

1  Eecherches,  pp.  234-236  ;  Comptes  Rendus,  XXIII.  p.  432. 

2  Astr.  Nachr.,  XXV.  p.  51. 

3  Berl  Vossische  Zeitung,  Sept.  25th,  1846. 

4  324°  58'. 

5  Comptes  Eendus,  XXIII.  pp.  959-  960,  etc. 

6  Ibid.,  p.  662. 

7  Astr.  Nachr.,  XXV.  p.  81. 


22  REPORT   ON   THE  HISTORY   OP 

name  and  symbol  have  not,  however,  generally  prevailed,*  as  they 
are  at  variance  with  the  received  nomenclature,  in  accordance 
with  which  the  names  of  Roman  deities  have  been  uniformly  select- 
ed ;  and  the  name  Neptune,  which,  with  its  appropriate  symbol 
(tJO,  a  trident,  was  originally  proposed1  by  the  Bureau  des  Lon- 
gitudes, and  immediately  adopted2  by  Gauss,  Struve,  Encke, 
and  Airy,  has  become  almost  universal. 

The  first  public  announcement  of  Mr.  Adams's  labors  was  in  a 
London  newspaper,3  the  Athenaeum.  In  this  journal,  under  date 
of  October  1st,  1846,  Sir  John  Herschel,  commenting  on  the 
actual  detection  at  Berlin  of  the  long-expected  planet,  spoke,  as 
before  quoted,  of  Bessel's  conversation  with  him,  and  subse- 
quent letter  in  1842,  and  alluded  to  the  fact  that  Mr.  Adams 4 
had  been  engaged  in  an  investigation  similar  to  that  of  Mr.  Le 
Verrier,  and  with  similar  results. 

On  the  13th  November,  the  Astronomer  Royal  presented  to 
the  Astronomical  Society  of  London  the  extremely  valuable  and 
important  Account  which  has  been  so  often  quoted  in  my  Report, 
and  which  must  ever  remain  an  integral  part  of  this  singular 
history.  Professor  Challis  presented  at  the  same  time  an  ac- 

*  It  seems  quite  desirable  that  astronomers  in  different  countries  should  be 
unanimous  in  the  adoption  of  fixed  names  and  symbols.  For  each  of  the  two 
planets  of  which  this  Report  speaks,  two  names  and  two  symbols  are  in  use. 
The  great  preponderance  of  authority  seems,  however,  decidedly  in  favor  of  the 
mythological  names  used  in  this  Report,  with  their  corresponding  symbols,  (J>  and 
y.  Le  Verrier,  who  in  1846  announced5  his  fixed  determination  to  call  Ura- 
nus by  the  name  of  its  discoverer,  according  to  Lalande's  proposition,  has  now 
happily  abandoned  6  this  unpopular  idea ;  and  even  the  distinguished  Arago,  who 
bestowed  the  name  of  the  French  geometer  upon  the  new  planet  discovered  in 
consequence  of  his  computations,  and  publicly  declared7  his  determination  never 
to  call  it  by  any  other  name  than  Le  Verrier,  has  yielded  to  the  general  usage 
of  astronomers. 

1  Le  Verrier,  letter  to  Galle,  Oct.  1,  1846,  Ast.  Nachr.,  XXV.  p.  194. 

2  Gauss,  letter  to  Encke,  Oct.  7,  1846,  Ibid.     Struve,  Bulletin  Imp.Acad.  Peters- 
burg, Dec.  27, 1846.     Challis,  Astr.  Nachr.,  XXV.  p.  313. 

3  London  Athenaeum,  Oct.  3,  1846,  p.  1019. 

4  See  also  Challis's  letter  of  Oct.  15,  in  London  Athenceum  of  Oct.  17,  1846. 

5  Recherches,  p.  3,  note. 

6  Comptes  Rendus,  XXVII.  pp.  209,  273,  et  al  7  Ibid.,  XXIII.  p.  662. 


THE   DISCOVERY   OF  NEPTUNE.  23 

count l  of  his  search  since  the  end  of  July ;  and  Mr.  Adams,  a 
brief  notice2  of  his  computations.  These  papers  are  printed 
together  in  the  Monthly  Notices  3  of  that  Society. 

During  the  month  of  November,  1846,  Le  Verrier  published 
a  complete  account  of  all  his  investigations,  giving  in  detail  the 
processes  by  which  he  had  arrived  at  the  results  previously  made 
known  in  the  Oomptes  Rendus.  This  memoir  may  justly  claim 
a  place  among  the  most  remarkable  mathematical  works  of  the 
age.  It  is  entitled  RecJiercJies  sur  les  Mbuvements  de  la  Planete 
Herschel,  dite  Uranus,  and  is  published  as  an  Addition  to  the 
Connaissance  des  Temps  for  1849,  occupying  256  pages.  Mr. 
Adams  gave  in  December  a  similar  abstract  of  his  computations, 
as  a  supplement  of  31  pages  to  the  Nautical  Almanac  for  1851. 

It  is  not  easy  for  those  who  are  not  versed  in  the  study  of 
Physical  Astronomy,  to  form  any  adequate  idea  of  the  difficulty 
of  the  problem  which  Messrs.  Le  Verrier  and  Adams  proposed 
to  themselves.  The  difficulties  in  the  development  of  the  prop- 
er methods  were  exceedingly  great,  as  any  one  might  infer  from 
the  manner  in  which  even  Airy  was  accustomed 4  to  speak  of  the 
problem.  An  investigation  must  indeed  be  eminently  difficult 
and  complicated,  which  that  distinguished  mathematician  would 
regard  as  unfeasible.  Not  only  the  orbit  and  mass  of  the 
suspected  planet,  but  the  elements  of  Uranus  also,  were  to  be 
regarded  as  unknown  quantities.  The  limits  of  error  of  the 
ancient  observations  were  also  undetermined,  but  must  yet  exer- 
cise an  important  influence  on  the  result. 

Le  Vender's  memoir  consists  of  three  parts.  The  first  of 
these 5  contains  a  complete  investigation  of  the  theory  of  Ura- 
nus, and  corresponds  to  the  first  paper  of  the  series  in  the  Comp- 
tes  Rendus.  It  is  an  investigation  of  the  highest  importance, 
apart  from  its  relation  to  the  problem  of  a  disturbing  planet,  and 
is  conducted  with  extraordinary  ability.  The  theory  of  Uranus 
may,  as  Airy  has  said,6  be  considered  as  placed  now  for  the  first 

1  Ast.  Soc.  Notices,  VII.  p.  145.  4    Airy's  "Account,"  passim. 

2  Ibid.,  p.  149.  5  Recherches,  §  2,  p.  6. 

3  Vol.  VII.  No.  9.  6  Account,  p.  131. 


24  REPORT   ON  THE   HISTORY   OP 

time  upon  a  satisfactory  foundation.  The  methods  used,  though 
essentially  those  of  Laplace,  Lagrange,  and  Poisson,  have  been 
modified  in  many  respects,  and  it  may  with  safety  be  asserted, 
that  almost  all  of  the  modifications  are  improvements. 

After  a  brief  consideration  of  the  general  formulas  of  pertur- 
bations, Le  Verrier  proceeds1  to  what  he  calls  the  simultane- 
ous determination  of  all  the  inequalities.  The  method  adopted 
is  such,  that  the  inequalities  are  all  obtained  at  the  same  time, 
and  are  so  mutually  dependent,  that  an  error  in  any  one  part 
of  the  calculation  vitiates  the  entire  result.  If,  then,  after  the 
numerical  computation  is  completed,  any  one  part  of  the  result 
is  found  to  be  exact,  it  may  fairly  be  concluded  that  the  remain- 
der is  exact  also.  By  this  method  of  "  simultaneous  determina- 
tion," Le  Verrier  determined2  all  the  perturbations  by  Saturn, 
carrying  them  out  to  the  very  smallest  sensible  terms ;  —  in 
many  cases  even  to  terms  whose  coefficients  amounted  only  to 
0".01.  The  planetary  elements 3  on  which  his  researches  were 
based,  were  taken  from  Bouvard's  tables. 

The  whole  computation  of  the  perturbations  by  Saturn  having 
been  completed,  Le  Verrier  proceeded  to  compute  4  a  part  of  the 
same  quantities  by  the  method  of  Lagrange,  in  order  to  test  the 
accuracy  of  his  previous  results.  The  actual  steps  of  this  sec- 
ond and  most  laborious  calculation  are  not  given,  but  the  agree- 
ment 5  between  the  amount  of  the  inequalities  as  obtained  by  the 
two  different  processes  is  wonderfully  close,  and  reflects  no  small 
honor  on  the  author's  powers  of  numerical  computation,  and  on 
the  precision  with  which  all  the  small  terms  were  taken  into 
account.  The  agreement  of  the  parts  thus  doubly  computed 
is  a  test  of  the  accuracy  of  the  whole  work. 

The  perturbations  by  Jupiter,  proportional  to  the  first  power 
of  the  mass,  are  determined6  according  to  the  ordinary  meth- 
ods ;  and,  although  not  doubly  computed,  as  in  the  case  of 
Saturn,  are  carried  out  with  great  rigor. 

1  Reckerches,  §  5,  p.  9.  4  Ibid ,  §  23,  p.  32. 

2  Rid.,  §  15,  p.  16.  5  Ibid.,  §§  26-28,  pp.  37  -41,  etc. 

3  Ibid.,  pp.  16,  52.  6  Rul,  §  34,  p.  51. 


THE   DISCOVERY   OF   NEPTUNE.  25 

In  the  investigation1  of  the  changes  proportional  to  the 
square  of  the  disturbing  force,  Le  Verrier  has  neatly  availed 
himself  of  the  method  used2  by  Laplace.  The  parts  of  these, 
which  are  not  strictly  secular,  can  without  hesitation  be  rejected, 
and  he  has  calculated3  the  values  of  the  coefficients  for  1800 
and  for  2300,  and  determined  their  values  for  intermediate  years 
by  simple  interpolation.  The  discussion  is  completed  by  the 
consideration4  of  the  influence  of  the  changes  of  Saturn's  ele- 
ments, produced  by  the  attraction  of  Jupiter.  This  is  investi- 
gated with  much  care  and  elegance.  The  action  of  Saturn,  as 
reflected  through  Jupiter,  is  not  of  sufficient  importance  to 
require  computation. 

The  theory  of  Uranus  was  thus  made  complete,  and  needs 
now  only  the  addition  of  the  perturbations  by  Neptune,  to 
accommodate  it  perfectly  to  the  present  demands  of  science. 

In  the  second  part 5  of  Mr.  Le  Terrier's  "  Researches,"  the 
theory  of  Uranus,  thus  remodelled,  is  compared  with  the  whole 
series  of  known  observations,  in  order  to  discover  how  large  the 
discrepancies  between  the  observed  and  computed  course  of  the 
planet  actually  were.  In  entering  upon  this  division  of  his 
subject,  the  author  shows6  that  the  sum  of  the  errors  in  the 
perturbations  as  given  by  Bouvard  —  considering  those  pertur- 
bations only  whose  value  had  completely  changed  during  the 
period  through  which  our  observations  extend,  and  making 
full  allowance  for  the  erroneous  masses  of  Jupiter  and  Saturn, 
which  Bouvard  used  —  amounted  to  twenty-nine  sexagesimal 
seconds. 

Bouvard's  tables  appear,  indeed,  throughout  this  part  of  the 
investigation,  in  a  singularly  unfavorable  light.  Le  Yerrier  has 
repeated7  the  whole  of  Bouvard's  computations,  and  subjected 
his  tables  to  a  most  searching  scrutiny.  The  result  must  have 
surprised  astronomers. 

1  Recherches,  §§  48  -  58.  5  Ibid.,  p.  89. 

2  Mean.  C6L,  Bowditch's  Trans.,  HI.  p.  283.  6  Ibid.,  §  61,  p.  90. 

3  Recherches,  p.  61 .  7  Ibid ,  pp.  91  -  99. 

4  Ibid.,  §  50,  p.  65. 

4 


26  REPORT   ON   THE   HISTORY   OF 

The  first  inaccuracy  alluded1  to  by  Le  Verrier  is  in  the  eccen- 
tricity of  the  orbit.  In  order  to  discover  the  value  of  the  eccen- 
tricity which  was  used  in  constructing  the  tables,  we  can  refer 
directly  to  Mr.  Bouvard's  Introduction,2  or  can  deduce  it  from 
the  table  3  of  the  equation  of  the  center.  These,  however,  do 
not  agree  with  one  another,  and  in  order  to  decide  which  of  them 
is  erroneous,  we  must  try,  if  possible,  some  third  method  of  find- 
ing the  eccentricity  assumed.  We  are  enabled  to  do  this  by  the 
algebraical  expression  of  the  equation  of  the  center,  which  is  also 
given4  in  the  preface.  But,  strange  to  say,  we  obtain  in  this 
way  still  a  third  value  differing  from  both  the  others.  The  ex- 
ample, which  Le  Yerrier  gives  5  to  illustrate  this,  is  the  value  of 
the  equation  of  the  center  for  a  mean  anomaly  of  90°. 


The  first  value  deduced  from  the  preface  is    .       .    5  93  57.52 
The  second     "          "          "         "        "  .5  92  71.04 

The  value  given  by  Table  X.  is    .        „  .   .  ,-x      .   5  93  48.00 

Mr.  Le  Verrier  assures  us,  farther,  that  any  attempt  to  decide 
definitely,  by  means  of  the  radius-vector,  what  was  the  true  eccen- 
tricity on  which  the  tables  were  based,  would  lead  only  to  the 
discovery  of  new  discordances. 

In  the  secular  motion  of  the  mean  longitude,  Tables  I.  and  II. 
do  not  agree.  The  error  in  Table  II.  would,  according  to 
Le  Verrier,  give  an  error  of  21".5  in  the  computed  place  for 
Flamsteed's  observation  of  1690.  In  the  formation  of  equations 
of  condition,  Bouvard  appears6  to  have  been  equally  unfortunate, 
both  as  regards  the  analytical  and  the  numerical  parts  of  the 
work.  Finally,  a  series  of  typographical  errors  is  given,7  sixteen 
of  them  being  in  the  single  table  of  the  equation  of  the  center, 
and  the  majority  of  them  errors  of  grave  importance. 

Le  Verrier  was  thus  compelled  to  repeat  the  whole  work,  and 
the  catalogue  of  errors  which  he  has  given  is  a  sufficient  indica- 

1  Eecherches,  p.  92.  5  Recherckes,  p.  93. 

2  Tables,  p.  ii.  6  Ibid.,  pp.  93  -  95. 

3  Table  X.  p.  95.  7  Ibid.,  pp.  96,  97. 

4  Tables,  p.  xv. 


THE   DISCOVERY   OF  NEPTUNE.  27 

tion  of  his  thoroughness  and  high  standard  of  precision.  And 
when  we  remember,  that  neither  Airy *  had  detected  these  errors, 
nor  Bessel  published  any  thing  concerning  them,  excepting  the 
notice  of  the  one  term  already  referred  to,  we  cannot  but  still 
more  admire  the  searching  rigor  of  Le  Verrier's  investigations. 

The  author  has  next  given  an  ephemeris  of  the  heliocentric2 
and  geocentric  3  places  of  Uranus  for  several  successive  days,  at 
the  epochs  of  the  ancient  observations,  and  of  those  modern  ones 
which  he  had  chosen  as  most  appropriate  for  the  comparison. 
For  these  latter  he  did  not  construct  normal  places,  but  selected 
a  series  of  two  hundred  and  sixty-two  of  the  best  observations, 
some  taken  in  opposition  and  some  in  quadrature,  and  suitably 
distributed  over  the  interval  between  1781  and  1845.  These, 
together  with  the  ancient  observations,4  were  then  compared 5 
with  the  theory.  The  comparisons  were  made  in  right-ascension 
and  declination,  and  the  differences  subsequently  converted  into 
differences  of  longitude  and  latitude.  Each  of  these  differences 
furnishes  one  equation,  but,  on  account  of  the  smallness  of  the 
errors  in  latitude,6  the  computation  was  founded  upon  the  longi- 
tudes alone ;  and  the  mean  equations  of  condition 7  used  were 
those  depending  upon  the  longitudes  after  grouping  together  all 
the  observations  made  at  the  same  period. 

By  means  of  these  Le  Verrier  was  enabled  to  solve  the  im- 
portant problem,8  —  "  Is  it  possible  to  satisfy  the  whole  of  the 
preceding  equations  by  a  proper  determination  of  the  values  of 
the  unknown  quantities  which  they  contain?"  He  found,  that 
the  elements,  furnished  even  by  those  equations  of  condition  de- 
rived solely  from  the  modern  observations,  were  entirely  incapa- 
ble 9  of  representing  the  course  of  the  planet  since  its  discovery ; 
—  the  discordance  in  the  mean  positions  deduced  from  ten  obser- 
vations in  the  years  1781  and  1782  amounting10  to  20.5  sexagesi- 

1  "Account?  p.  126.  6  Eecherches,  p.  137. 

2  Recherches,  §  71,  pp.  100  -  110.  1  Ibid.,  pp.  138  - 141. 

3  Ibid.,  §  73,  pp.  112-124.  8  Ibid.,  p.  142. 

4  Specially  reduced,  pp.  124-126,  §  74.  9  Ibid.,  §  79,  p.  144. 

5  Recherches,  §  77,  pp.  129  -  136.  10  Rid.,  p.  143. 


28  REPORT   ON   THE  HISTORY   OF 

mal  seconds.  It  is  impossible  to  believe  that  such  an  error  ac- 
tually exists,  and  we  thus  see  that  the  theory  is  inadequate. 

The  same  result  is  obtained  by  considering  the  data  from  two 
other  entirely  different  points  of  view.  In  the  first  place,  the 
consideration1  of  the  equations  of  condition  formed  from  the 
observations  at  eight  equidistant  epochs,  comprehending  an  inter- 
val of  ninety-eight  years,  and  of  the  relations  between  their 
second  differences,  shows  2  that  the  resulting  values  of  the  varia- 
tion of  the  mean  motion  are  totally  incompatible  with  one  another, 
and  that  some  change  in  the  then  existing  theory  was  inevitably 
necessary.  Secondly ,  from  the  relation  between  the  correction 
of  the  elements,  the  mean  anomaly  at  the  epoch,  and  the  error 
of  the  heliocentric  longitude,  Mr.  Le  Terrier  forms 3  eighteen 
equations  of  condition ;  and,  by  an  extremely  elegant  process,4 
deduces  the  amount  of  discordance  between  theory  and  observa- 
tion, which  could,  under  the  worst  possible  combination  of  unfa- 
vorable circumstances,  result  from  the  errors  to  which  the  obser- 
vations are  subject.  He  allows5  to  each  of  the  normal  places 
from  modern  observations  a  possible  error  of  four  seconds,  and  to 
the  position  deduced  from  Flamsteed's  three  observations  in  1715, 
a  possible  error  of  fifteen  seconds.  But  even  by  assuming  all 
the  errors  at  their  maximum,  and  all  acting  to  diminish  the  dis- 
crepancy, Le  Verrier  shows  that  only  92"  out  of  356"  can  be  ac- 
counted for,  leaving  a  discordance  of  264  sexagesimal  seconds 
still  unexplained.6 

In  the  third  part7  of  the  work,  which  corresponds  to  the  sec- 
ond memoir8  in  the  Oomptes  Rendus,  the  author  proceeds  to  the 
discussion  of  the  great  problem  of  the  cause  of  the  anomalies 
which  he  had  proved  to  exist.  In  introducing  this  part  of  the 
Researches  by  some  remarks  on  the  difficulty  of  the  problem, 
Le  Verrier  remarks,9  that  the  unforeseen  obstacles  which  he 


1  Recherches,  §  80.  6  Recherches,  p.  150. 

2  Ibid.,  p.  146.  7  Ibid.,  p.  151. 

3  Ibid.,  p.  147,  §  81.  *  C.  R.,  XXII.  p.  907. 

4  Ibid.,  §§  82,  83,  pp.  147  -  149.  9  Recherches,  p.  151. 

5  Ibid.,  pp.  149,  150. 


THE   DISCOVERY   OF  NEPTUNE.  29 

encountered  would  more  than  once  have  deterred  him  from  the 
farther  prosecution  of  his  labor,  had  he  not  been  fully  impressed 
with  a  conviction  of  its  importance.  The  readers  of  the  work 
cannot  but  be  struck  with  this  remark,  for  the  impediments  en- 
countered and  the  apparent  contradictions  of  the  results  would 
indeed  have  dismayed  any  less  gifted  mathematician.  Entering 
upon  the  immediate  subject,  the  author  considers l  in  a  cursory 
manner  various  hypotheses  which  have  been  suggested  to  ac- 
count for  the  apparently  anomalous  motion  of  Uranus,  and 
assigns  his  reasons  for  rejecting  them.  Astronomers  must  als*o 
be  impressed  with  the  argument2  which  his  computations  had 
furnished  him,  against  the  hypothesis,  that  a  comet  might  have 
produced  the  disturbances  in  question.  It  is,  that  both  the 
series  of  ancient  observations  and  that  of  the  observations  since 
1820  are  alike  incapable  of  according  with  elements  deduced 
from  the  motion  of  the  planet  for  the  forty  years  immediately 
following  its  discovery ;  in  other  words,  that  between  1690  and 
1845  two  perturbations  had  occurred.  As  regards  the  hypothe- 
sis of  an  unknown  planet,  too,  he  inferred  that  it  could  not  be 
within  the  orbit  of  Uranus,  as  its  effect  on  Saturn  must,  in  that 
case,  have  been  more  perceptible.  "It  is  easy  to  conclude," 
said3  he,  "  that  its  perturbative  action  would  only  be  exerted  at 
the  particular  time  when  it  passed  in  the  neighborhood  of  Ura- 
nus, and  the  small  difference  which  there  would  be  between  the 
periods  of  revolution  of  the  two  bodies  would  prevent  this  cir- 
cumstance from  having  taken  place  more  than  once  in  the  period 
which  the  observations  of  the  planet  include.  This  consequence 
is  contradictory  to  our  deduction  from  the  observations.  The 
period  comprised  between  1781  and  1820  shows  no  trace  what- 
ever of  large  perturbations  ;  and,  on  the  other  hand,  can  neither 
be  connected  with  the  previous  nor  with  the  subsequent  observa- 
tions." 

This  last  was  unquestionably  written  after  the  researches  were 
completed.     The  planet  of  Le  Verrier's  theory  must  have  acted 

1  Recherches,  §  86.  2  Ibid.,  p.  152. 

3  Ibid.,  p.  153;   C.  R.,  XXII.  p.  914. 


30  REPORT   ON  THE  HISTORY   OF 

on  Uranus  twice  during  the  interval  comprised  between  the 
observations  of  1690  and  1845.  But  it  is  now  known  that 
only  one  maximum  of  perturbation  by  Neptune  occurred  within 
that  period,  namely,  in  1822.  With  regard  to  the  fact  that  the 
observations  between  1781  and  1820  were  capable  of  being  per- 
fectly represented  by  elliptic  elements,  the  question  naturally 
arises,  whether  osculating  elements  might  not  be  found,  capable 
of  representing  the  motions  of  Uranus  for  any  period  of  forty 
years,  within  moderate  limits  of  error. 

In  case  the  perturbing  body  be  exterior  to  Uranus,  Mr.  Le  Ver- 
rier  showed x  that  it  could  not  be  at  any  very  remote  distance, 
such,  for  example,  as  three  times  the  mean  distance  of  Uranus  ; 
for,  in  that  case,  the  mass  to  be  attributed  must  be  so  large  as  to 
affect  Saturn  very  much  more  than  the  theory  of  that  planet 
allows  us  to  assume.  It  is  most  natural,  then,  to  commence  the 
first  rough  approximation,  by  assuming  the  new  distance  to  be 
about  double  that  of  Uranus,  —  and  the  more  so,  as  this  distance 
would  correspond  to  the  curious  empirical  formula  2  of  Wurm,  Ti- 
tius,  and  Bode,  which  represented,  though  in  a  very  rough  way, 
the  distances  of  the  planets  from  the  sun.  Le  Verrier  is  entitled 
to  praise  for  holding  himself  independent  of  this  "  law,"  which, 
as  Gauss  long  since  showed,3  is  not  only  totally  devoid  of  that 
precision  which  characterizes  nature's  laws,  but  fails  entirely 
when  legitimately  applied  to  Mercury.  As  it  is,  perhaps  the  in- 
fluence of  this  ill-omened  formula  may  have  been  instrumental  in 
depriving  both  Le  Verrier  and  Adams  of  the  satisfaction  of  ar- 
riving, by  theoretical  means,  at  a  knowledge  of  the  elements  and 
mass  of  Neptune,  and  thus  making  a  physical  as  well  as  a  math- 
ematical discovery. 

The  problem  to  be  considered  was  fortunately  simplified,  in 
some  degree,  by  the  fact,  that  the  perturbations  in  latitude  were 
very  small.  Uranus  moves  in  a  plane  but  slightly  inclined  to 
the  ecliptic,  and  the  same  must,  therefore,  in  all  probability,  be 

1  Recherches,  p.  153. 

2  Bode,  Bed.  Astr.  Jahrb.,  1791,  p.  188.    Lalande,  Bibliographie,  p.  845. 

3  Monatliche  Corresponded,  VI.  p.  504. 


THE  DISCOVERY  OF  NEPTUNE.  31 

true  of  the  disturbing  body.  Le  Verrier,  then,  assuming  that 
the  unknown  planet  moved  in  the  ecliptic,  proceeded  to  investi- 
gate the  following  questions 1 :  — 

"  Is  it  possible  that  the  irregularities  of  Uranus  are  due  to  the 
action  of  a  disturbing  planet ,  situated  in  the  ecliptic  at  a  mean 
distance  double  that  of  Uranus?  And  if  so,  where  is  this  planet 
situated  ?  What  is  its  mass  f  What  are  the  elements  of  the 
orbit  ivhich  it  describes?" 

There  is,  as  he  says,  but  one  route  to  follow  in  the  discussion 
of  this  question.  "  It  is  necessary2  to  form  expressions  for  the 
perturbations,  due  to  the  new  body,  in  functions  of  its  mass  and 
of  the  unknown  elements  of  the  ellipse  which  it  describes ;  we 
must  introduce  these  perturbations  into  the  coordinates  of  Ura- 
nus, calculated  by  means  of  the  unknown  elements  of  the  ellipse 
which  this  planet  describes.  Putting  the  coordinates,  thus  ob- 
tained, equal  to  the  coordinates  observed,  we  must  take  as  un- 
known quantities  in  the  resultant  equations  of  condition,  not  only 
the  elements  of  the  ellipse  described  by  Uranus,  but  also  the 
elements  of  the  ellipse  described  by  the  disturbing  planet  whose 
position  we  seek." 

Taking,  then,  not  the  planet's  coordinates,  but  the  elements  of 
its  orbit,  as  the  unknown  quantities,  Le  Verrier  follows3  the 
course  thus  indicated,  using  the  common  formulas,  and  omitting 
all  consideration  of  the  terms  proportional  to  the  time  which  can 
be  confounded  with  the  mean  motion,  and  of  the  constants  which 
can  be  combined  with  the  epoch.  The  first  attempt  at  a  solution 
was  based  upon  eight  equations4  similar  to  those  5  to  which  we 
have  before  alluded.  These  were  founded  on  observations6  sub- 
sequent to  1747,  all  of  Flamsteed's  observations  being  neglected. 
The  second  differences  were  combined  precisely  as  before.  The 
six  equations  7  thus  obtained  were  reduced,  by  a  dexterous  elim- 
ination8 of  the  epoch,  eccentricity,  and  mean  motion,  to  three 

1  C.  R.,  XXII.  p.  915  ;  Recherches,  p.  154.  3  Ibid.,  §  80. 

2  Recherches,  p.  154,  §  88.  6  Ibid.,  p.  146. 

3  Rid.,  §§  90-95.  7  Rid.,  p.  162. 

4  Rid.,  p.  162,  §  96.  8  Rid.,  p.  164. 


32  REPORT   ON  THE  HISTORY   OP 

others,1  whose  constant  terms  were  the  same  as  those  in  the 
equations  above  alluded  to.  From  these  he  obtained2  ^yVir 
(m  =  2.11)  as  a  first  approximation  to  the  mass.  But  from  the 
numerous  obstacles  to  accuracy  which  are  manifest  in  the  course 
of  this  solution,  Le  Verrier  inferred  3  that  the  interval  of  ninety- 
eight  years  was  not  sufficient  for  his  purpose,  but  that  it  was 
necessary  to  extend  the  interval  as  far  as  observations  would  per- 
mit, and  to  form  the  equations  of  condition  with  all  possible 
rigor. 

This  is  done  in  the  second  solution,4  —  a  solution  which  is  pre- 
eminently a  discussion  of  limits,  and  a  brilliant  combination  of 
ingenuity,  of  analytical  skill,  and  of  laborious  calculation,  —  a 
solution  which  cannot  be  adequately  described  without  departing 
from  the  popular  form  prescribed  to  me  in  this  Report.  Account 
is  taken  of  all  the  allowable  errors  in  the  ancient  observations, 
and  "  the  field  of  inquiry  narrowed  with  consummate  skill."  5 
The  epoch  being  assumed  at  the  beginning  of  the  present  cen- 
tury, all  the  values  of  its  mean  longitude  which,  when  substi- 
tuted in  the  equations  of  condition,  would  give  a  negative  mass, 
as  well  as  those  which  would  give  a  mass  large  enough  to  affect 
Saturn  sensibly,  were  promptly  rejected.6  The  expression  ob- 
tained for  the  mass  is  in  the  form  of  a  fraction ; 7  the  numerator 
and  denominator  of  which  were  separately  examined,  the  former 
by  an  elegant  application  of  Sturm's  formula.  The  result 8  was, 
that  the  longitude  of  the  epoch  must  be  included  between  the 
limits  97°  and  190°,  or  between  263°  and  359°,  in  order  to 
render  the  corresponding  mass  positive ;  and  if  those  masses  be 
rejected  which  the  motion  of  Saturn  forbids  us  to  assume, 
Le  Verrier  found9  that  the  longitude  of  the  epoch  must  be  com- 
prised between  108°  and  162°,  or  between  297°  and  333°. 
But,  after  laborious  calculation,  he  also  found  that  neither  of 


1  Recherches,  p.  164.  6  Recherches,  p.  169. 

2  Ibid.,  §  100.  7  Ibid-,  §§  104-107. 

3  Ibid.,p.  165.  8  Rid.,  p.  174. 

4  Rid.,  §§  101-124.  9  Ibid.,  §  112,  p.  181. 

5  Peirce,  Proc.  Amer.  Acad.,  I.  p.  66. 


THE   DISCOVERY   OF  NEPTUNE.  33 

these  limitations  will  allow  the  places  in  1690  and  1747  to  be 
represented  with  tolerable  accuracy,  "  so  that  the  consequence 
which  would  seem  to  result  from  the  discussion,  thus  conducted, 
would  be,  that  it  was  impossible  to  represent  the  course  of  Ura- 
nus by  means  of  the  perturbative  action  of  the  new  planet." 

Le  Verrier  was  fortunately  undismayed  by  this  result,  although 
many  a  good  mathematician  and  experienced  computer  would, 
for  less  reason,  have  abandoned  his  apparently  unprofitable  labor 
in  despair.  But  even  Le  Verrier,  according  to  Biot,1  revolved 
the  matter  in  his  mind  for  three  months  without  advancing  a 
step.  He  discovered  subsequently,  as  he  next  states,2  that, 
by  neglecting  two  little  inequalities  of  the  longitude,  in  them- 
selves so  small  that  one  would  suppose  himself  warrantable  in 
omitting  them  with  perfect  impunity,  all  the  details  of  the  solu- 
tion became  different,  and  the  errors  in  1690  were  completely 
changed.  He  found,3  still  farther,  that  in  spite  of  the  apparent 
limitations  furnished  above  by  the  resulting  negative  value  of  the 
mass,  the  assumption  of  values  outside  these  limits,  for  the  longi- 
tude of  the  epoch,  enabled  him  perfectly  to  represent  the  motions 
of  Uranus.  He  arrived,  in  short,  at  the  fundamental  proposition,4 
"  that  there  was  in  the  ecliptic  but  one  single  region  in  which 
the  perturbing  planet  could  be  placed,  so  as  to  account  for  the 
motions  of  Uranus  ;  that  the  mean  longitude  of  this  planet  on  the 
1st  of  January,  1800,  must  have  been  betzveen  243°  and  252°." 
Continuing  his  numerical  computations,  and  calculating,5  for  each 
one  of  the  eighteen  normal  places,  the  values  of  the  perturba- 
tions corresponding  to  different  hypotheses  as  to  the  longitude  of 
the  epoch,  Le  Verrier  found6  "  that  all  the  observations  of  Ura- 
nus could  be  represented  by  means  of  the  perturbative  action  of 
a  planet  whose  mean  longitude  was  252°  on  the  1st  of  January, 
1800,  and  whose  eccentricity  and  perihelion  longitude  are  deter- 
mined by  the  formulas"  already  given.  The  corresponding 
longitude  in  1847.0  would  be  325°,  and,  as  above  stated,  Le  Ver- 

1  Journal  des  Savans,  Jan.,  1847.  4  Ibid.,  §  114,  p.  185. 

2  Recherckes,  p.  181.  5  Ibid.,  §  116,  pp.  187, 188. 

3  Ibid.,  p.  182.  6  Ibid.,  p.  193. 


34  EEPORT  ON  THE  HISTORY  OF 

rier  closed  his  memoir  of  June,  1846,  by  expressing  his  hope 
that  astronomers  might  detect  the  planet. 

The  fourth  book1  contains  a  more  precise  determination  of  the 
elements  of  the  orbit,  and,  though  the  processes  are  given  more 
in  detail,  is  essentially  the  same  as  the  memoir  of  August  31,  in 
the  Comptes  JRendus.2  In  this  book  the  limits  of  the  real  and 
the  apparent  place  of  the  disturbing  body  are  computed  with 
still  greater  precision.  The  hypotheses  as  to  the  mean  dis- 
tance vary3  from  36.2  to  39.2;  those  as  to  the  longitude  of 
the  epoch,  from  234°  to  270°.  For  these  different  hypoth- 
eses, six  in  number,  the  coefficients  of  the  equations  of  condi- 
tion are  minutely  computed.4  Thirty-three  equations  of  condi- 
tion are  formed  5  by  comparison  with  observed  geocentric  places, 
From  these  equations  six  unknown  quantities,  and  among  them 
the  elements  of  the  orbit  of  Uranus,  are  eliminated,  and 
their  places  supplied  by  the  unknown  quantities  representing 
the  corrections  of  the  mean  distance,  and  of  the  longitude 
of  the  epoch.  The  resulting6  thirty-three  are  solved7  by  the 
method  of  least  squares,  and  give,8  as  the  final  solution,  the 
orbit  on  page  21  of  this  Report. 

Le  Verrier,  in  thus  assigning  definitely  the  planet's  position  in 
the  heavens,  expressed  9  the  belief,  that  its  disc  would  be  large 
enough  to  indicate  its  planetary  character  to  the  attentive  ob- 
server. Uranus,  at  the  distance  19,  has  an  apparent  diameter 
of  4".  Assuming  a  position  and  mass  of  the  new  planet  con- 
formable to  his  computations,  and  its  density  the  same  as  that 
of  Uranus,  Le  Verrier  inferred,  that  its  apparent  diameter  in  op- 
position must  be  about  3".  3,  and  its  specific  brilliancy  about  one 
third  that  of  Uranus. 

The  orbit  and  mass  thus  obtained  represent  all  the  ancient 
observations  within  eight  seconds,  except  Flamsteed's  in  1690,  to 

1  Recherches,  p.  196.  6  Ibid.,  §  135,  p.  231. 

2  C.  R.,  XXIII.  p.  428.  7  Ibid.,  §  136,  p.  233. 

3  Recherches, p.  198.  8  Ibid.,  §§  137-141,  pp.  234-236. 

4  Ibid.,  §  130,  pp.  203-220.  9  Ibid.,  p.  237;  C.  R.,  XXIII,  p.  430. 

5  Ibid.,  §  131,  p.  222. 


THE   DISCOVERY   OF  NEPTUNE.  35 

which  Le  Verrier  allows l  but  little  weight,  being  content  with 
representing  it  within  20".* 

The  author  next  determines  2  the  extreme  limits  within  which 
the  disturbing  planet  is  necessarily  situated,  allowing3  a  large 
error  to  all  the  observations,  —  five  seconds,  for  instance,  to  the 
modern  ones,  and  twenty-five  to  Flamsteed's  in  1690.  The  re- 
sult is,4  that  the  mean  distance  must  be  between  the  limits  35.04 
and  37.9.  Assuming  the  corresponding  times  of  revolution  as 
the  extreme  limits  of  the  period,  he  finds,5  by  an  ingenious  geo- 
metrical process,  the  limits  of  the  planet's  place,  which  they  give 
for  184T. 

The  fifth  and  last  part 6  of  the  Researches  corresponds  to  the 
memoir  presented  to  the  Academy  of  Sciences  on  the  5th  of  Oc- 
tober, after  the  discovery  of  the  planet,  but  was  evidently  written 
before  the  welcome  news  had  reached  Mr.  Le  Verrier.  In  this 
he  endeavors  to  deduce  from  the  perturbations  of  the  latitude 
the  position  of  the  place  in  which  the  new  planet  must  move.  He 
infers7  that  the  observations  in  latitude  concur  with  those  in 
longitude  in  indicating  the  existence  of  a  disturbing  planet,  that8 
the  plane  of  this  planet's  orbit  must  be  inclined  about  4°  38'  to 
that  of  the  orbit  of  Uranus,  and  that9  a  single  observation  of 
the  orbit  of  this  new  body  would  suffice  to  make  known  approxi- 
mately the  plane  in  which  it  moves.  These  deductions  as  to  the 
plane  of  the  orbit  Le  Yerrier  submitted  with  much  diffidence, 
on  account  of  the  smallness  of  the  perturbations  in  latitude  from 
which  they  must  be  made. 

Mr.  Adams's  investigation  is  of  a  totally  different  nature, 
though  characterized  by  remarkable  ability  and  mathematical 


*  In  order  to  do  justice  to  this  observation,  it  must  be  stated  that  Neptune, 

with  the  mass  19540,  used  by  Prof.  Peirce,  satisfies 10  this  observation  within  a 
single  second. 

1  Recherches,  p.  238.  6  Ibid.,  p.  250. 

2  Ibid.,  §§  143-148.  7  Rid.,  p  251. 

3  Ibid.,  p  240,  §  143.  8  Ibid.,  p.  251. 

4  Ibid.,  p.  240,  §  144.  9  Ibid.,  p.  252. 

5  Ibid.,  pp.  242,  247.  10  Proc.  Amer.  Acad.,  I.  333. 


36  KEPORT   ON   THE    HISTORY   OF 

power.  In  it  the  question  of  limits  is  neither  discussed,  nor  in 
the  least  degree  involved,  but  the  problem  is  directly  proposed, 
—  "To  find  the  most  probable  orbit  and  mass  of  the  disturbing 
body  which  has  acted  on  Uranus."  The  question,  whether  it  be 
necessary  to  assume  the  existence  of  such  a  body,  is  not  dis- 
cussed. The  labors  of  Bouvard  were  supposed  to  have  set  this 
question  at  rest.  Mr.  Adams  states,1  that  his  first  solution  was 
attempted  in  1843,  assuming  the  orbit  to  be  a  circle,  the  dis- 
tance, nearly*  in  conformity  with  "  Bode's  law,"  2  twice  that  of 
Uranus,  and  taking  solely  the  modern  observations  into  account. 
The  errors  of  the  tables  were  taken  3  from  Bouvard's  equations 
of  condition  as  far  as  the  year  1821,  and,  for  later  dates,  from 
Schumacher's  Astronomische  Nachrichten  and  the  Reductions 
of  the  Greenwich  Planetary  Observations. 

Mr.  Adams  inferred4  from  his  results  that  a  good  general 
agreement  between  theory  and  observation  might  be  obtained, 
and  therefore  commenced5  a  more  accurate  investigation,  the 
results  of  which  were  communicated  to  the  Astronomer  Royal  in 
the  letter  6  of  October,  1845,  above  7  referred  to,  and  to  Prof. 
Challis,  some  time  8  in  the  month  of  September. 

Flamsteed's  observation  of  1690  was  entirely  rejected.9  The 
chief  inequalities  given  by  Bouvard  were  recomputed,10  without 
the  detection  of  any  error,  excepting  the  one  pointed  out  by 
Bessel.  Airy's  mass  of  Jupiter  u  was  introduced  in  the  place  of 
the  one  used  by  Bouvard.  Those  inequalities  depending  on  the 
square  of  the  disturbing  force,  which  had  been  pointed  out  by 
Hansen,  were  also  recomputed.12  The  differences  between  the 
calculated  and  observed  heliocentric  longitudes  were  converted  13 


1  "Explanation?  §  3,  p.  4.  8  "  Account?  p.  128,  letter  No.  6. 

2  Bed.  Astr.  Jahrb.,  1791,  p.  189.  9  Rid.,  p.  130.    "Explanation?  §  25. 

3  Expl,  §  4.  10  "  Explanation?  p.  5,  §  7. 

4  Ibid.,  §  3.  "  Mem.  R.  Astr.  Soc.,  X.  p.  47. 

5  Ibid.,  §  10  et  seq.  12  Expl,  p.  6. 

6  "Account?  p.  129.  13  Ibid.,  p.  7,  §  9. 

7  Expl,  p.  15. 


THE   DISCOVERY   OF  NEPTUNE.  3T 

into  differences  of  mean  longitude.  Observations  made  near  op- 
position were  selected,1  when  possible,  and  the  series  of  mod- 
ern observations  divided  into  groups,  from  which  were  deduced  2 
normal  places  at  intervals  of  three  years.  The  equations  of  con- 
dition formed  from  these  served  as  the  basis  of  the  entire  com- 
putation. 

Assuming,  then,  as  a  first  hypothesis,3  the  mean  distance  of 
the  new  body  to  be  twice  that  of  Uranus,  Adams  computes  4  the 
value  of  the  fundamental  perturbations.  The  values  obtained  5 
are  almost  identical  with  those  6  of  Le  Verrier.  But  with  regard 
to  the  influence  of  the  third  and  fourth  terms,  Adams  does  not  ap- 
pear to  have  experienced  the  inconveniences  by  which  Le  Verrier 
states  that  he  was  so  much  impeded.7  Both  mathematicians 
agree,8  however,  in  the  rejection  of  the  small  perturbations  of  the 
second  order,  dependent  on  the  square  of  the  eccentricity  of  the 
disturbing  planet.  Taking  the  mean  opposition  in  1810,  as  the 
epoch,  Mr.  Adams  has  elegantly  arranged 9  his  equations  of 
condition  in  such  a  way,  that  they  separate  themselves  into  two 
groups,  each  having 10  but  five  unknown  quantities.  The  coeffi- 
cients are  then  readily  computed  by  summation.  By  eliminat- 
ing n  the  unknown  quantities  in  each  group,  it  will,  therefore, 
be  comparatively  easy,  for  any  assumed  value  of  the  mass  and 
longitude  at  the  epoch,  to  obtain  a  correction  by  the  method  of 
least  squares.  But  as  the  unknown  quantities  are  the  same  in 
all  the  equations  of  each  group,  these  equations  may  be  added,12 
and  the  substitution  of  the  elements  of  Uranus,  already  approxi- 
mately known,  gives  values  for  the  mass  and  epoch.  The 
equations  of  condition  drawn  from  the  ancient  observations, 
omitting  that  in  1690,  are  the  snued  3  for  the  determination  of 

Explanation,  p.  5,  §  6.  9  Expl,  §  13. 

Ibid.,  pp.  6,  7.  10  Ibid.,  $  14. 

Ibid.,  p.  8,  §  12.  "  Ibid.,  §§  15-20. 

Ibid.,  §  12.  '2  2bid.,  §  21,  p.  13. 

Ibid.,  p.  9.  13  Rid.,  §  23. 
Recherches,  p.  161,  §  95. 
Ibid.,  p.  181. 
8  Adams, Expl §§  11,  12;  Le  Verrier,  RechercJies,  pp.  158,201. 


30  REPORT   ON  THE  HISTORY   OF 

the  eccentricity  and  perihelion  longitude.  This  determination  is 
very  skilfully  made,  and  the  elements l  furnished  by  the  whole 
analysis  are  those  communicated 2  to  the  Astronomer  Royal  in 
October,  1845. 

Mr.  Adams  next  proceeded  3  to  repeat  the  whole  investigation, 
assuming  the  mean  distance  to  be  37.25,  the  first  hypothesis 
having  been  38.36.  For  the  time  when  the  computations  on 
this  hypothesis  were  made,  no  date  is  assigned.  They  were 
probably  made  during  the  summer  of  1846,  as  the  resulting  ele- 
ments were  communicated  4  to  Mr.  Airy  on  the  2d  of  September 
of  that  year.  They  are  as  follows  5  :  — 

Epoch,          .       ..^ 1810.328 

Mean  longitude, 264°  50' 

Longitude  of  perihelion,          ....      298°  41' 

Eccentricity,      ,         '.....         .         .         .         0.120615 

Mean  longitude,  Oct.  6,  1846,         .         .         .      323°    2' 
Mass,  .         .       ^ 

The  theoretical  corrections  of  the  mean  longitude  on  each 
hypothesis  are  next  6  given,  —  the  parts  due  to  the  changes  in 
the  elements  of  Uranus  and  to  the  action  of  the  hypothetical 
planet  being  written  separately,  —  and  these  corrections  are 
compared  with  observation. 

The  modern  observations  of  Uranus  are  thus  admirably  rep- 
resented7 down  to  the  year  1840.  The  ancient  ones  were 
represented  within  tolerable  limits,  excepting  the  observation  in 
1771,  where  the  discrepancy  amounts  to  11". 8  on  the  first, 
and  12". 8  on  the  second  hypothesis.  Le  Verrier  has  not  given 
any  comparison  of  this  observation  with  his  final  orbit.8 

In  the  observations  since  1840,  however,  Mr.  Adams  did  not 
find  so  satisfactory  an  agreement.  The  differences,  as  deduced 
from  the  three  oppositions  immediately  preceding  the  investiga- 
tion, were  9  by  the  two  hypotheses,  — 

1  Expl,  §  31.  6  Rid.t  §§  49-51. 

2  12.  Ast.  Soc.  Notices,  pp.  129,  151.  7  Ibid.,  §  52. 

3  Expl,  §  32,  et  seq.  s  Recherches,  §  142,  p.  238. 

4  12.  Ast.  Soc.  Not.,  VII.  pp.  138, 151.  9  Expl,  §  53,  p.  28. 

5  Expl,  §§47,  48,  p.  25. 


THE  DISCOVERY   OF   NEPTUNE.  39 

I.  II. 

1843,  7!ll  5.77 

1844,  8.79  7.05 

1845,  12.40  10.18 

The  errors  for  these  three  years  are,  thus,  about  one  fifth  less 
in  the  second  hypothesis.  The  first  had  assumed  that  the  ratio 
of  the  mean  distances  of  the  two  planets  was  equal  to  sin.  30°, 
the  second  that  it  was  sin.  31°.  Mr.  Adams  roughly  inferred  1 
from  this  consideration,  that  the  true  ratio  would  be  about  equal 
to  sin.  35°,  which  gives  a  mean  distance  of  33.42. 

The  application  of  the  Rule  of  Three  to  a  problem  so  compli- 
cated as  that  which  the  orbit  of  the  disturbing  planet  presented 
was,  we  are  bound  to  believe,  intended  merely  as  a  rude  means 
of  conjecture.  It  appears,  therefore,  surprising,  that  this  infer- 
ence should  be  dwelt  upon  as  one  of  the  merits  of  Mr.  Adams's 
investigation,  and  as  tending  to  show  that  the  solution  at  which 
he  arrived  corresponded  to  the  orbit  and  place  of  Neptune. 
Even  had  Mr.  Adams  intended  to  apply  the  rule  of  simple  pro- 
portion, it  is  impossible  that  he  should  have  founded  it  upon  the 
comparison  of  three  oppositions  alone.  Le  Verrier  has  shown  2 
that  the  assumption  of  even  35  as  the  mean  distance  would  lead 
to  intolerable  discordances.  Peirce  has  further  proved  3  that  an 
important  change  in  the  character  of  the  perturbations  takes 
place  near  the  distance  35.3.  It  is,  therefore,  evident  that  no 
claims  can  be  based  upon  the  rough  inference  alluded  to.  And 
it  is  but  just  to  assume  that  Mr.  Adams  would  disclaim  any  in- 
tention to  dwell  upon  this  point,  although  stress  has  been  laid 
upon  it  4  by  one  of  the  most  eminent  of  his  countrymen. 

After  giving  the  formulas  for  the  corrections  of  the  tabular 
radius-vector  of  Uranus  upon  each  of  his  hypotheses,  Mr.  Adams 
closes  by  stating,5  that,  on  account  of  the  shortness  of  the  pe- 


1  Expl,  p.  29 ;  "  Account?  p.  139. 

2  Recherches,  p.  240. 

3  Proc.  Amer.  Acad.,  I.  66 . 

4  Herschel,  Outlines  ofAstr.,~p.  517,  note. 

5  Expl,  §  60. 


40  REPORT   ON   THE   HISTORY    OF 

riod  (98  years,  the  observation  in  1690  having  been  rejected), 
and  the  smallness  of  the  perturbations  in  latitude,  all  his  at- 
tempts to  fix  the  plane  of  the  orbit  had  been  unsatisfactory. 

I  have  thus  endeavored  to  give  an  account  of  the  origin  and 
progress  of  the  theory  of  Uranus  up  to  the  discovery  of  Nep- 
tune, and  the  publication  of  those  computations  which  had  led 
astronomers  to  suspect  its  existence  and  direction.  Of  the  discus- 
sion concerning  priority  which  unfortunately  arose,  it  is  not  neces- 
sary to  speak.  There  cannot  be  the  slightest  doubt  of  the  fact, 
that  the  several  investigators  were  entirely  independent  of  one 
another ;  but  as  many  persons,  especially  those  not  professedly 
devoted  to  the  pursuit  of  science,  attach  importance  to  the  ques- 
tion of  priority,  I  have  endeavored  to  state  the  facts  as  im- 
partially as  possible,  and  thus  to  give  the  data  by  which  any 
one  may  be  enabled  to  judge  for  himself.  The  discussion  which 
subsequently  arose  was  of  such  a  nature  as  to  throw  the  con- 
troversy between  the  partisans  of  the  French  and  of  the  English 
geometer  entirely  into  the  background. 

Before  passing  from  the  discovery  of  Neptune  to  the  subse- 
quent development  of  the  theory,  it  is  proper  to  allude  to  the 
charts  published  by  the  Berlin  Academy  at  the  instance1  of 
Bessel ;  inasmuch  as  these  furnished  the  means  by  which  Nep- 
tune was  discovered  at  Berlin  upon  the  first  search.  They  have 
also  directly  contributed,  within  the  last  four  years,  to  the  detec- 
tion of  several  members  of  our  solar  system.  The  chart2  em- 
bracing the  region  in  which  Neptune  was  found  had  been  drawn 
up  with  great  accuracy  by  Dr.  Bremiker,  the  eminent  coadjutor 
of  Prof.  Encke,  in  the  Berlin  Astronomical  Almanac.  Although 
sometime  printed,  it  had  been  published  but  a  short  time.  Had 
Prof.  Challis  been  in  possession  of  this  map,  he  would  probably  3 
have  discovered  Neptune  on  the  4th  of  August,  as  he  observed 
it  as  a  fixed  star  on  that  day,4  while  sweeping  for  the  planet. 

1  Abhandl  d.  Kdnigl  Akad.  Berl.,  1824,  p.  iii.;  Astr.  Nachr.,  IV.  pp.  297,  437. 

2  Hour  XXI. 

3  Astr.  Nachr.,  XXV.  p.  102 ;  Ast.  Soc.  Not.,  VII.  p.  146. 

4  Ast.  Soc.  Not.,  VII.  p.  148. 


THE  DISCOVERY   OF  NEPTUNE.  41 

He  observed  it  again,  August  12.  He  also  noted  it  September 
29,  as  seeming  to  have  a  disc ;  but  the  news  of  the  discovery 
at  Berlin  on  the  23d  arrived  before  the  next  fair  evening.1 

The  slowness  of  the  planet's  motion  of  course  rendered  it  im- 
possible to  find  the  true  orbit,  till  after  the  lapse  of  considerable 
time,  but  elements  upon  the  hypothesis  of  a  circular  orbit  were 
computed  within  the  first  month  by  Adams,2  Galle,3  and  Binet.4 
These  agreed  very  nearly  with  one  another,  and  coincided  espe- 
cially in  showing  the  distance  from  the  sun  to  be  about  30.  Mr. 
Adams  afterwards  computed  5  a  second  circular  orbit,  which  gave 
the  same  result. 

Mr.  Valz,  of  the  Marseilles  Observatory,  endeavored  6  early  in 
the  year  1847  to  deduce  the  form  of  the  orbit  from  the  small  arc 
described  by  the  planet  since  its  discovery.  He  found  himself, 
however,  unable  to  obtain  a  reliable  value  for  the  eccentricity, 
but  assigned  &  as  the  result  of  his  computations.  At  the  same 
time  he  requested  attention  to  the  fact,  that,  in  a  letter  to  Arago 
concerning  the  perturbations  of  Halley's  comet,  published  7  Sept. 
12,  1835,  he  had  expressed  his  belief  in  the  existence  of  a 
planet  exterior  to  Uranus. 

The  means  of  obtaining  elliptic  elements  was  afforded  by  the 
fortunate  discovery  of  an  ancient  observation  of  Neptune.  This 
discovery  was  made  independently  by  two  astronomers,  Mr. 
Walker  in  "Washington,  and  Dr.  Petersen  in  Altona,  each  of 
whom  computed  an  approximate  ephemeris  for  Neptune,  and 
came  to  the  conclusion  that  no  observer  except  Lalande  had 
catalogued  in  the  vicinity  of  the  planet. 

The  modes  of  research  employed  by  Dr.  Petersen  and  Mr. 


1  Ast.  Soc.  Notices,  VII.  p.  147. 

2  Astr.  Nachr.,  XXV.  p.  106. 

3  Ibid.,  XXV.  pp.  192,  311 ;  Bericht  d.  KOnigl.  Preuss.  ATcad.,  1846,  p.  280;  Ast. 
Soc.  Not.,  VII.  p.  148  ;  Astr.  Nachr.,  XXV.,  p.  311. 

4  Comptes  Rendus,  XXIII.  p.  798. 

5  Ast.  Soc.  Not.,  VII.  p.  148. 

6  Comptes  Rendus,  XXIV.  p.  638. 

7  Ibid.,  I.  p.  130. 

6 


42  REPORT   ON   THE  HISTORY  OF 

Walker  were  essentially  different.  Dr.  Petersen1  compared  a 
chart  of  the  stars  of  the  Histoire  Celeste,  in  a  zone  extending 
from  2°  south  to  4°  north  latitude,  and  from  14h-  to  17h<  right- 
ascension,  directly  with  the  heavens,  and  found  that  three  stars 
observed  by  Lalande  were  no  longer  visible.  On  a  second  com- 
parison, he  saw  that  the  recorded  places  of  two  of  these  were 
probably  vitiated  by  a  typographical  error  of  one  minute  of 
time.  The  third  star  had  been  observed  May  10th,  1795,  and 
was  entered  2  as  follows  in  the  Histoire  Celeste  :  — 

Mag.  Middle  Thread.  Zen.  Dist. 

7.8         14h-  llm-  23s-.5        60°  7  19" 

Dr.  Petersen  then  calculated  from  Galle's  circular  elements  the 
position  of  Neptune  for  the  time  of  this  observation,  and  found 
an  agreement  sufficiently  close  to  convince  him  that  the  missing 
star  was  Neptune. 

Walker  had,  in  the  United  States,  arrived  at  the  same  result 
by  a  totally  different  investigation.3  He  made  no  use  of  the 
telescope.  He  had  at  hand  a  large  collection  of  observations, 
from  which  he  had  already  computed  elements  of  sufficient  accu- 
racy to  show  that  Lalande  had  only  swept  in  the  neighborhood 
of  Neptune  upon  the  8th  and  10th  of  May,  1795.  For  these 
nights  he  computed  a  locus  of  Neptune,  by  assuming  different 
eccentricities,  upon  the  two  hypotheses  of  the  present  true  anom- 
aly being  greater  or  less  than  180°.  The  catalogue  of  La- 
lande's  stars  within  this  locus  was  then  subjected  to  a  rigid  scru- 
tiny. The  stars  which  have  been  since  observed,  those  more 
than  15'  north  or  south  of  the  planet's  computed  path,  and 
those  below  the  ninth  magnitude,  being  rejected,  there  remained 
but  one  star  in  the  list,  and  that  was  less  than  a  minute  north  of 
the  computed  declination  of  Neptune  for  that  right-ascension. 
This  discovery  was  made  on  the  2d  of  February,  and  on  the 
next  day  Mr.  Walker  communicated  to  the  astronomers  of  the 

1  Astr.  Nachr.,  XXV.  pp.  291,  303. 

2  Histoire  Ctteste,  p.  158,  obs.  8. 

3  Washington  Union,  Feb.  9,  1846;  Proc.  Am.  Phil.  Soc.,  IV.  p.  318;    Proc. 
Amer.  Academy,  I.  p.  57 ;    Astr.  Nachr.,  XXV.  p.  383. 


THE   DISCOVERY    OF    NEPTUNE.  43 

Washington  Observatory  his  conviction  that  the  missing  star  was 
Neptune.  Upon  the  4th,  the  weather  first  became  clear,  and 
Prof.  Hubbard  of  the  Observatory  had  the  gratification  of  find- 
ing l  that  the  star  was  no  longer  in  the  place  where  Lalande  had 
seen  it. 

It  was  thus  rendered  a  moral  certainty,  by  the  independent 
labors  of  the  American  and  the  German  astronomer,  that  Nep- 
tune had  been  observed  by  Lalande,  and  that  the  eccentricity  of 
the  orbit  was  very  small.  This  enabled  Mr.  Walker  to  compute 
elliptic  elements 2  during  the  month  of  February,  1847,  which 
represented  the  motion  of  the  planet  with  great  accuracy  ;  and 
Mr.  Adams  also  communicated  3  elliptic  elements  to  Prof.  Schu- 
macher, under  date  of  May  19th.  By  means  of  the  epheni- 
erides  of  Neptune  published 4  by  these  two  astronomers,  the 
planet  was  followed  without  difficulty  through  the  opposition  of 
184T. 

Mr.  Walker  and  Dr.  Petersen  had  both  immediately  written 
to  Le  Yerrier  to  inform  him  of  their  researches,  and  Le  Verrier 
communicated  to  the  French  Academy  of  Sciences,  at  the  same 
meeting,5  the  results  of  the  investigations  at  Washington  and  at 
Altona. 

But  in  speaking  of  Mr.  Walker's  elements,  he  remarked  6  that 
"  the  small  eccentricity  which  appeared  to  result  from  Mr. 
Walker's  computations  would  be  incompatible  with  the  nature  of 
the  perturbations  of  the  planet  Herschel." 

The  hypotheses  of  Walker  and  Petersen  received  a  striking 
confirmation  from  the  examination  of  Lalande's  MSS.  by  Mr. 
Mauvais,  of  the  Royal  Observatory,  Paris.  Mauvais  discovered7 
that  Lalande  had  observed  the  star  on  the  8th,  as  well  as  on 

Proc.  Amer.Acad.,  I.  p.  64  ;  Proc.  Am.  Phil  Soc.,  IV.  p.  318. 
Proc.  Amer.  Acad,  I.  p.  67 ;  Proc.  Am.  Phil.  Soc.,  IV.  p.  319 ;  Astr.  Nachr., 
XXV.  p.  383. 

Astr.  Nachr.,  XXV.  p.  399.    See  also  R.  Ast.  Soc.  Not.,  June  11,  1847. 
Astr.  Nachr.,  XXV.  pp.  51,  241. 
March  29,  1847. 
Comptes  Rendus,  XXIV.  p.  531. 
7  Comptes  Rendus,  XXIV.  p.  641 ;  Astr.  Nachr.,  XXVI.  p.  97. 


44  REPORT   ON   THE   HISTORY    OF 

the  10th  of  May.  But  in  consequence  of  the  non-accordance  of 
the  two  observations,  he  had  only  inserted  the  latter  in  the  His- 
toire  Celeste,  and  annexed  to  it  the  (:)  which  he  used  to  denote 
a  doubtful  observation.  Both  Mauvais  and  Peiree,  after  a  care- 
ful reduction  of  both  observations,  found l  that  the  discordance 
corresponded  precisely  to  the  motion  of  Neptune  in  two  days,  — 
so  that  the  question  of  identity  is  now  beyond  dispute. 

Meantime,2  Prof.  Peirce  had  taken  a  remarkable  step.  From 
the  distance,  30,  and  consequent  angular  motion,  without  any 
hypothesis  as  to  the  character  of  the  orbit,  he  arrived  at  the 
startling  conclusion,3  "  that  the  planet  Neptune  is  not  the  planet 
to  which  geometrical  analysis  had  directed  the  telescope ;  that 
its  orbit  is  not  contained  within  the  limits  of  space  which  have 
been  explored  by  geometers  searching  for  the  source  of  the  dis- 
turbances of  Uranus ;  and  that  its  discovery  by  Galle  must  be 
regarded  as  a  happy  accident." 

This  conclusion,  paradoxical  as  it  might  at  first  have  appeared 
to  many,  was  announced  with  a  candor  and  moral  courage  only 
equalled  by  that  of  Le  Verrier  in  his  original  prediction  of  the 
planet's  place.  The  reasoning4  by  which  Peirce  defended  his 
position  deserves,  even  at  this  late  day,  the  most  careful  consider- 
ation. It  is  so  clear  and  convincing,  that  it  would  seem  unneces- 
sary to  dwell  upon  it,  were  it  not  that  even  now  astronomers  5  of 
high  eminence  do  not  hesitate  to  dispute  the  ground  there  taken  ; 
although  the  arguments  adduced  against  it  are  rather  of  a  popu- 
lar than  of  a  mathematical  character. 

Peirce  first  alluded  6  to  the  two  fundamental  propositions  of  Le 
Verrier,  viz. :  — 

1st.  That  the  planet's  mean  distance  must  be  between  35  and 
37.9; 


1  Comptes  Rendus,  XXIV.  p.  666  ;  Proc.  Amer.  Acad.,  I.  p.  149. 

2  March  16,  1847. 

3  Proc.  Amer.  Acad.,  I.  p.  65. 

4  Ibid.,  pp.  65-68. 

5  Herschel,  Outlines  of  Astronomy,  §  776,  p.  516. 

6  Proc.  Amer.  Acad.,  I.  p.  66. 


THE   DISCOVERY   OF   NEPTUNE.  45 

2d.  That  the  mean  longitude  for  January  1st,  1800,  must 
have  been  within  the  limits  243°  and  252° ; 
and  announced  that  he  had  convinced  himself  that,  although 
neither  of  these  was  inconsistent  with  the  observations  made  upon 
Neptune  since  its  discovery,  yet  that  the  two  combined  were  ut- 
terly irreconcilable  with  observation  ;  —  that  if  the  first  proposi- 
tion were  assumed  as  true,  the  mean  longitude  in  1800  must 
have  been  at  least  forty  degrees  from  the  limits  of  the  second ; 
—  and  that,  if  we  adopted  the  second  proposition,  the  time  of 
revolution  must  be  less  by  forty  years  than  the  inferior  limit  giv- 
en by  the  first. 

"  It  is  not,  however,"  continued  Peirce,  "  a  necessary  conclu- 
sion that  Neptune  will  not  account  for  the  perturbations  of  Ura- 
nus ;  for  its  probable  mean  distance  of  about  30  is  so  much  less 
than  the  limits  of  the  previous  researches,  that  no  inference  from 
them  can  be  extended  to  it.  An  important  change,  indeed,  in  the 
character  of  the  perturbations,  takes  place  near  the  distance 
35.3  ;  so  that  the  continuous  law  by  which  such  inferences  are 
justified  is  abruptly  broken  at  this  point,  and  it  was  hence  an 
oversight  in  Mr.  Le  Verrier  to  extend  his  inner  limit  to  the  dis- 
tance 35.  A  planet  at  the  distance  35.3  would  revolve  about  the 
sun  in  210  years,  which  is  exactly  two  and  a  half  times  the  period 
of  revolution  of  Uranus.  Now  if  the  times  of  revolution  of  two 
planets  were  exactly  as  2  to  5,  the  effects  of  their  mutual  influ- 
ence would  be  peculiar  and  complicated,  and  even  a  near  approach 
to  this  ratio  gives  rise  to  those  remarkable  irregularities  of  motion 
which  are  exhibited  in  Jupiter  and  Saturn,  and  which  greatly 
perplexed  geometers  until  they  were  traced  to  their  origin  by 
Laplace.  This  distance  of  35.3,  then,  is  a  complete  barrier  to 
any  logical  deduction,  and  the  investigations  with  regard  to  the 
outer  space  cannot  be  extended  to  the  interior. 

"  The  observed  distance,  30,  which  is  probably  not  very  far 
from  the  mean  distance,  belongs  to  a  region  which  is  even  more 
interesting  in  reference  to  Uranus  than  that  of  35.3.  The  time 
of  revolution  which  corresponds  to  the  mean  distance  30.4  is  not 
168  years,  being  exactly  double  the  year  of  Uranus,  and  the 


46  REPORT   ON   THE   HISTORY   OF 

influence  of  a  mass  revolving  in  this  time  would  give  rise  to  very 
singular  and  marked  irregularities  in  the  motions  of  this  planet. 
The  effect  of  a  near  approach  to  this  ratio  in  the  mean  motion  is 
partially  developed  l  by  Laplace  in  his  theory  of  the  motions 
of  the  three  inner  satellites  of  Jupiter.  The  whole  perturbation 
arising  from  this  source  may  be  divided  into  two  portions  or  ine- 
qualities, one  of  which,  having  the  same  period  with  the  time  of 
revolution  of  the  inner  planet,  is  masked  to  a  great  extent  behind 
the  ordinary  elliptic  motions,  while  the  other  has  a  very  long  pe- 
riod, and  is  exhibited  for  a  great  length  of  time  under  the  form  of 
a  uniform  increase  or  diminution  of  the  mean  motion  of  the  dis- 
turbed planet." 

Peirce  closed  this  most  important  paper  by  showing,2  that,  if 
the  period  of  Neptune  were  more  than  166|,  and  less  than  169| 
years,  the  conclusion  was  inevitable,  that  its  period  was  precisely 
twice  as  long  as  that  of  Uranus. 

Walker  has  since  found3  the  period  of  Neptune  to  be  164.6 
years.  The  two  periods  are  therefore  not  precisely  commensu- 
rable, but  they  approach  commensurability  so  nearly  that  some  of 
the  terms  4  of  the  perturbations  of  Uranus  require  careful  investi- 
gation, which,  according  to  the  theories  of  Le  Verrier  and  Ad- 
ams, would  be  merged  in  the  longitude  of  the  epoch  and  other 
elements  of  the  elliptic  motion. 

In  reference  to  the  apparent  inconsistency  of  the  assertion, 
that  the  discovery  was  "  a  happy  accident,"  Peirce  still  farther 
showed  5  that  the  problem  was  susceptible  of  several  solutions,  de- 
cidedly different  from  one  another,  and  from  those  of  Le  Verrier 
and  Adams,  and  equally  complete  with  theirs.  "  The  present 
place  of  the  theoretical  planet,"  to  quote  from  his  communica- 
tion6 of  May  4th,  1847,  to  the  American  Academy,  "  which 


1  Mtcanique  Ctleste,  Bowditch's  Transl.,  I.  p.  656  ;  IV.  p.  126. 

2  Proc.  Amer.  Acad.,  I.  p.  68. 

3  Smithsonian  Contributions,  II.  App.  I.  p.  6. 

4  Proc.  Amer.  Acad.,  I.  p.  334. 

5  Boston  Courier,  April  30, 1847. 

6  Proc.  Amer.  Acad.,  I.  p.  144. 


THE   DISCOVERY   OF   NEPTUNE.  47 

might  have  caused  the  observed  irregularities  in  the  motions  of 
Uranus,  would,  in  two  of  them,  be  about  one  hundred  and  twen- 
ty degrees  from  that  of  Neptune,  the  one  being  behind,  and  the 
other  before,  this  planet.  If  Le  Verrier  or  Adams  had  fallen 
upon  either  of  the  above  solutions  instead  of  that  which  was  ob- 
tained, Neptune  would  not  have  been  discovered  in  consequence 
of  geometrical  prediction.  The  following  are  the  approximate 
elements  for  the  three  solutions,  at  the  epoch  of  January  1st, 
1847 :  — 

I.  II.  III. 

Mean  longitude,        .         .     fc.         319°  79°  199° 

Longitude  of  perihelion,       .         .     148°  219°  188° 

Eccentricity,            .         .         .         0.12  0.07  0.16 

In  each  of  these  the  mass  is  0.0001187,  and  the  period  of  side- 
real revolution  double  that  of  Uranus." 

Continuing  the  investigation,  Prof.  Peirce  arrived  at  another 
singular  result.  He  found  himself  unable  to  reconcile  the  ob- 
served motions  of  Neptune  with  the  assumption,  that  it  was  the 
chief  source  of  the  unexplained  irregularities  in  the  motion  of 
Uranus.  This  result  was  in  all  candor  acknowledged  to  the 
Academy,  but  with  the  remark 1  that  he  considered  "  it  would 
be  presumptuous  in  him  to  claim  for  his  investigations  a  free- 
dom from  error  which  the  greatest  geometers  have  not  escaped, 
especially  in  the  face  of  the  vastly  improbable  conclusion  to 
which  his  analysis  tended."  He  subsequently  2  succeeded,  as  is 
well  known,  in  entirely  explaining  the  motions  of  Uranus  by  the 
action  of  Neptune,  using  the  mass  ^fa.  The  failure  of  the  first 
attempt  was  in  consequence  of  his  not  having  carried  the  devel- 
opment of  the  disturbing  function  to  a  sufficient  number  of 
terms,  but  having  contented  himself  in  the  first  approximation 
with  the  number  of  terms  used  3  by  Le  Verrier  in  his  formulas. 
The  numerical  formulas  of  Le  Verrier's  Researches  can  only 


1  Proc.  Amer.  Acad.,  I.  p.  145. 

2  Ibid ,  I.  p.  332. 

3  Recherches,  §  94. 


48  REPORT   ON  THE  HISTORY   OF 

apply  to  mean  distances  within  the  limits  assigned  by  that  geom- 
eter. 

During  the  summer  of  1847,  Peirce  determined  the  approxi- 
mate perturbations  of  Neptune  by  the  other  planets,  and  com- 
municated *  them  to  Walker  in  November.  Walker,  using  these 
values,  deduced  a  pure  elliptic  orbit,  from  the  discussion  of  689 
observations,  including  those  of  Lalande.  This  orbit,2  together 
with  the  normal  places  on  which  it  was  founded,  and  with  the 
expressions  for  the  heliocentric  coordinates,  was  presented  to  the 
American  Academy,  December  7th.  At  the  same  meeting, 
Peirce  communicated3  the  corresponding  values  of  the  entire 
perturbations  of  Neptune  up  to  the  terms  depending  on  the 
cubes  of  the  eccentricities.  He  used  the  masses  of  the  planets 
assumed  by  Le  Verrier  in  his  theories  of  Mercury  and  Uranus, 
with  the  exception  of  the  mass  of  Uranus,  for  which  he  took  La- 
ment's determination.4  The  results  were  given  both  in  the 
usual  form  and  in  that  which  Le  Verrier  had  adopted  in  his 
theory  of  Mercury.  Peirce  also  gave  5  the  particular  values  of 
the  perturbations  of  the  true  anomaly  and  radius-vector,  for 
the  epoch  of  Lalande's  observations,  and  for  every  three  months 
from  October,  1846,  to  January,  1851.  Through  the  labors  of 
Peirce  and  Walker,  the  elliptic  orbit  of  Neptune,  with  the  numer- 
ical values  of  its  perturbations  by  all  the  other  planets,  was  thus 
known  at  the  beginning  of  December,  1847,  with  such  accuracy, 
that  an  ephemeris  6  founded  on  these  data  satisfied  the  observa- 
tions of  September,  1848,  within  one  and  a  tenth  seconds  of 
time  in  righteiscension,  and  six  and  a  half  seconds  in  declina- 
tion.7 

Applying  anew  Peirce's  second  values  for  the  perturbations, 


1  Proc.  Amer.  Acad.,  I.  p.  285. 

2  Ibid. ;  Proc.  Amer.  Phil  Soc.,  IV.  378. 

3  Proc.  Amer.  Acad.,  I.  pp.  287-295. 

4  Mem.  R.  Ast.  Soc.,  XL  p.  59. 

5  Proc.  Amer.  Acad.,  I.  pp.  294,  295. 
e  Astr.  Nachr.,  XXVII.  p.  347. 

7  Ibid.,  XXIX.  p.  191. 


THE  DISCOVERY   OP   NEPTUNE.  49 

and  using  still  later  observations,  Walker  presented,1  March  6, 
1848,  a  second  pure  elliptic  orbit,  which  has  represented 2  the 
course  of  Neptune  so  well  up  to  the  present  time,  as  to  render  a 
nearer  approximation  unnecessary,  if  indeed  it  were  possible. 

The  perturbations  of  Uranus  by  Neptune  were  also  communi- 
cated3 by  Prof.  Peirce  on  March  6th.  This  geometer  had 
found 4  Neptune  capable  of  entirely  accounting  for  all  the 
motions  of  Uranus,  provided  a  mass  of  about  goooo  ^e  adopted. 

The  determination  of  the  mass  has  been  a  problem  of  some 
difficulty.  Soon  after  the  discovery  of  the  planet,  Mr.  Lassell, 
of  Liverpool,  discovered 5  a  satellite.  Observations  of  this 
satellite,  made  at  Pulkowa,  at  Liverpool,  and  at  Cambridge, 
have  given  masses  *  for  Neptune  differing  very  considerably 
from  one  another.  The  question  must  be  expected  to  remain 
unsettled  for  some  time.  Peirce  seems  to  have  provisionally 
adopted  the  mass  (19540)  deduced  by  him  from  Cambridge  ob- 
servations alone. 

The  following  table  6  of  differences  between  the  observed  and 
calculated  longitudes  of  Uranus  is  taken  from  Peirce's  commu- 
nication, and  shows  how  well  the  motions  of  this  planet  now  ac- 
cord with  theory.  The  first  column  contains  the  discrepancies 
which  exist  when  the  action  of  Neptune  is  not  taken  into  consid- 
eration. The  second  and  third  give  those  which  would  remain, 
did  the  theoretical  planets  of  Le  Verrier  and  Adams  actually 
exist,  and  act  upon  Uranus.  The  third  column  contains  the  dis- 
crepancies, after  allowing  for  the  influence  of  Neptune,  suppos- 
ing the  mass  to  be  that  deduced  by  Peirce  from  the  Cambridge 
observations  alone. 

*  Struve  found  from  Pulkowa  observations  14596-  Peirce,  from  English  and 
American  observations,  igygo  5  from  American  observations  alone,  isko- 

1  Proc.  Amer.  Acad.,  I.  p.  331. 

2  Smithsonian  Contrib.  to  Knowl.,  II.,  Appendix  I.  p.  5. 

3  Proc.  Amer.  Acad.,  I.  p.  334. 

4  Ibid.,  p.  332. 

5  Astr.  Nachr.,  XXVI.  p.  165. 

6  Proc.  Amer.  Acad.,  I.  p.  333. 

7 


)0  REPOKT   ON   THE   HISTORY   OF 

RESIDUAL   DIFFERENCES   BETWEEN  THE  THEORETICAL   AND   OB- 
SERVED  LONGITUDES   OF  URANUS. 


Date. 

Without  any  ex- 
terior Planet. 

By  Le  Vender's 
Theory,  with 

By  Adams's 
Theory,  with 

Introducing   Nep- 
tune with  Peirce's 

Mass  =  5335- 

Mass  =  ^. 

Mass  =  jgig. 

1845, 

+  6.5 

// 

+  10.2 

// 

—  0  Q 

1840, 

+  0.7 

+  2.2 

+  1.3 

—  1.1 

1835, 

—  4.5 

—  0.8 

—  1.2 

+  2.0 

1829, 

—  7.8 

—  2.2 

+  2.0 

+  0.8 

1824, 

—  7.6 

—  5.4 

+  1.7 

—  2.0 

1819, 

+  3.8 

+  0.4 

—  2.2 

+  1.0 

1813, 

+  4.5 

—  0.9 

—  1.0 

—  0.3 

1808, 

+  3.8 

+  0.8 

0.0 

—  0.4 

1803, 

—  3.4 

+  0.8 

+  1.6 

+  0.8 

1797, 

—  6.7 

—  1.0 

—  0.5 

+  0.3 

1792, 

—  7.8 

+  0.3 

—  1.1 

+  0.3 

1787, 

+  2.0 

—  1.2 

—  0.2 

—  0.5 

1782, 

+  20.5 

+  2.3 

0.0 

—  3.0 

1 

[1769, 

+  123.3 

+  3.7 

+  1.8 

—  6.0 

I 

1756, 

+  230.9 

—  4.0 

—  4.0 

+  4.0 

1 

1715, 

+  279.6 

+  5.5 

—  6.6 

+  8.7 

1 

1690, 

+  289.0 

—  19.9 

+  50.0 

+  0.8 

Beside  that  solution  of  the  "  inverse  problem  of  the  perturba- 
tions of  Uranus,"  which  Le  Verrier  and  Adams  obtained,  we 
have  seen  that,  using  their  data,  there  are  a  number  of  other 
solutions,  one  of  which  corresponds  to  the  orbit  and  mass  of  Nep- 
tune. Had  Le  Verrier  been  in  possession  of  observations  inter- 
mediate to  those  which  he  used,  he  would  not  have  arrived  at  so 
harmonious  results.  The  fact,  however,  that  Neptune  does  not 
correspond  to  his  solution,  cannot  in  the  least  detract  from  the 
merit  or  intrinsic  value  of  his  investigations.  These  may  be 
looked  upon  as  a  complete  discussion  of  two  distinct  problems. 

In  the  first  place,  Le  Verrier  demonstrated  the  existence  of  a 
disturbing  planet.  He  solved  this  problem  completely  by  prov- 
ing, not  only  that  it  was  impossible  to  represent  the  motions  of 
Uranus  without  the  assumption  of  some  unknown  disturbing 
body,  but  that  the  perturbations  were  of  that  analytical  form 


THE  DISCOVERY  OF  NEPTUNE.  51 

which  belongs  to  the  influence  of  an  exterior  planet.  In  so  far 
as  this  goes,  Le  Verrier  may  be  considered  the  discoverer  of 
Neptune. 

In  his  solution  of  the  second  problem,  that  of  the  orbit  and 
mass,  he  was  not  so  successful.  But,  inasmuch  as,  by  using  all 
the  observations  within  his  reach,  he  found  an  orbit  and  mass 
capable  of  accounting  for  the  observed  motions  of  Uranus,  he 
must  be,  in  the  opinion  of  mathematicians,  legitimately  entitled 
to  all  the  admiration  which  he  would  have  received  had  such  a 
planet  actually  moved  in  that  orbit.  He  omitted,  it  is  true,  the 
consideration  of  the  terms  depending  on  a  near  approach  to  com- 
mensurability ;  but  this,  although  certainly  a  defect,  cannot  be 
considered  as  an  error  in  the  theory,  for,  within  the  limits  where 
he  had  reason  to  suppose  that  the  orbit  was  situated,  these  terms 
are  almost  uniformly  negligible.  His  laborious  and  elegant  re- 
searches have  been  crowned  with  brilliant  success,  and  Mr.  Le 
Verrier  himself  rewarded  by  the  consciousness  of  having  been 
the  immediate  occasion  of  the  discovery  of  Neptune.  And  al- 
though the  agreement  of  Neptune's  direction  at  the  time  of 
discovery  with  the  direction  of  the  theoretical  planet  was  but 
accidental,  it  almost  seems  as  though  the  heavens  strove  to 
show  themselves  propitious,  so  happy  was  the  accident,  so  won- 
derful the  coincidence. 

In  order  to  show  as  clearly  as  possible  the  relative  positions  of 
Neptune,  and  of  the  theoretical  planets  of  Le  Verrier  and 
Adams,  I  have  computed  the  following  table,  which  gives  the 
true  longitude  and  the  radius-vector  of  each  of  the  three,  for 
every  tenth  year  of  the  two  centuries  immediately  succeeding 
Flamsteed's  first  observation  of  Uranus.  It  will  be  observed 
from  this  table,  that  the  longitude  of  the  planet  of  Le  Vender's 
theory  coincided  with  that  of  Neptune  in  1840 ;  and  that  Nep- 
tune would  be  in  conjunction  with  Adams's  planet  about  the  year 
1856.  The  closest  agreement  of  the  radius-vectors  was  not  far 
from  the  year  1830,  and  the  greatest  discordance  in  the  years 
from  1710  to  1720,  at  which  time  the  distance  of  Neptune  was 


52 


REPORT  .ON   THE   HISTORY   OF 


about  midway  between  that  of  Uranus  and  that  of  the  two  hy- 
pothetical planets. 


TRUE  LONGITUDE. 

RADIUS-  VECTOR. 

Date. 

Neptune. 

Le  Verrier. 

Adams. 

Neptune. 

Le  Verrier. 

Adams. 

1690, 

34l!l 

0 

65.1 

81?3 

29.92 

39.09 

40.69 

1700, 

4.4 

79.2 

94.5 

29.84 

39.63 

41.30 

1710, 

26.7 

93.0 

107.3 

29.79 

40.89 

41.66 

1720, 

49.1 

106.5 

119.8 

29.77 

40.04 

41.74 

1730, 

70.8 

120.2 

132.0 

29.80 

39.85 

41.48 

1740, 

93.8 

134.0 

145.5 

29.86 

39.40 

41.09 

1750, 

116.0 

148.2 

158.9 

29.95 

38.71 

40.39 

1760, 

138.0 

163.0 

172.6 

30.04 

37.84 

39.46 

1770, 

160.1 

178.9 

187.3 

30.10 

36.93 

38.37 

1780, 

181.8 

195.1 

202.7 

30.22 

35.68 

37.15 

1790, 

203.5 

212.7 

219.2 

30.28 

34.58 

35.91 

1800, 

225.9 

231.4 

236.8 

30.30 

33.57 

34.74 

1810, 

246.8 

251.2 

255.5 

30.28 

32.78 

33.75 

1820, 

268.5 

270.9 

275.2 

30.23 

32.64 

33.06 

1830, 

290.2 

291.4 

295.5 

30.15 

32.29 

32.77 

1840, 

312.0 

312.0 

315.9 

30.02 

32.63 

32.91 

1850, 

334.2 

332.0 

335.9 

29.96 

3332 

33.47 

1860, 

356.4 

351.0 

355.0 

29.87 

34.26 

34.37 

1870, 

18.7 

8.9 

14.1 

29.81 

35.43 

35.49 

1880, 

41.1 

25.8 

29.9 

29.77 

36.48 

36.73 

1890, 

63.4 

39.4 

45.7 

29.78 

37.99 

37.97 

Mr.  Adams  has  taken  no  personal  part  in  the  controversies 
which  have  arisen  since  the  discovery  of  Neptune,  but  has  con- 
tinued to  devote  himself  to  the  pursuit  of  science.  Mr.  Le  Ver- 
rier has  published 1  several  articles  in  the  Oomptes  Rendus,  in 
order  to  defend  his  claim  to  be  considered  the  actual  discoverer 
of  Neptune,  by  showing  that  this  planet  might  have  been  brought 
within  the  limits  of  his  theory.  In  England,  Sir  John  Herschel 
has  taken  2  similar  ground  in  favor  of  Mr.  Adams. 


1  Comptes  Rendus,  1848,  Sept.  llth,  Oct.  2d,  etc. 

2  Outlines  of  Astronomy,  pp.  309,  509-512,  516  -518. 


THE   DISCOVERY   OF  NJEPTUNE.  53 

The  argument  of  Le  Verrier  is,1  that,  since  he  was  obliged  to 
found  his  computations  upon  irregularities,  which,  on  account  of 
the  probable  inaccuracy  of  the  observations,  were  uncertain  by  a 
tenth  part  of  their  whole  value,  it  would  be  very  natural  that 
this  want  of  precision  should  affect  the  positions  thence  deduced 
for  the  disturbing  planet,  and  that  these  positions  should  them- 
selves be  wrong  by  their  tenth  part. 

I  should  not  have  alluded  to  this  reasoning  had  not  Mr.  Le 
Verrier  published  it,  and  it  will  perhaps  even  now  be  considered 
unadvisable  to  endeavor  to  refute  it.  According  to  this  argu- 
ment, an  error  of  3.0  would  be  allowable  in  the  mean  distance 
30,  —  of  4.0  if  the  mean  distance  were  40,  etc.,  —  errors  which 
would  make  the  attraction  of  the  planet  to  be  exerted  in  a  direc- 
tion totally  different  from  the  true  one.  But  even  this  allow- 
ance would  not  correct  the  error  of  the  radius-vector  in  1710 
and  1890. 

As  a  rejoinder  to  the  last  argument,  Mr.  Le  Verrier  says,2  that, 
"  when  there  are  perturbations,  he  can  tell  where  Neptune  is," 
but  to  demand  that  he  "  should  do  it  long  after  the  perturbative 
action  has  disappeared,  is  simply  to  exact  of  him  what  is  impossi- 
ble, —  a  species  of  miracle."  Yet  at  the  time  of  the  early  ob- 
servations, when  the  radius-vector  of  Neptune  differed  from  that 
of  the  theoretical  planet  by  ten  times  the  radius  of  the  earth's  orbit, 
Uranus  was,  according  to  Mr.  Le  Vender's  theory,  undergoing 
a  perturbation  by  Neptune.3  It  is  unnecessary  to  allude  in  this 
connection  to  Le  Verrier's  deduction 4  from  his  computations,  that 
the  small  eccentricity  of  Neptune's  orbit  would  be  incompatible 
with  the  nature  of  the  perturbations  of  Uranus. 

With  regard  to  the  mass,  Le  Verrier  uses  a  somewhat  differ- 
ent argument.  Assuming  the  mass  to  be,  as  Peirce  has  found, 
T5^  of  what  had  been  predicted,  he  shows 5  that  this  corresponds 
to  an  error  of  but  a  fifth  in  the  diameter  of  Neptune.  This  is 
very  true,  — no  schoolboy  will  deny  it,  — but  it  was  the  mass, 

1  Comptes  Rendus,  XXVII.  p.  273.         *  Comptes  Rendus,  XXIV.  p.  531. 

2  Ibid.,  p.  275.  5  jbid.,  XXVII.  p.  277. 

3  SeeHerschel's  Outlines  of  Astronomy,  p.  517,  §  776. 


54  REPORT   ON   THE  HISTORY   OF 

not  the  diameter,  which  he  sought.  He  has  farther  alluded ]  to 
the  fact,  that,  even  now,  astronomers  are  in  doubt  concerning 
the  exact  mass  of  Uranus,  inasmuch  as  the  masses  deduced  from 
its  action  on  Saturn  and  from  the  periods  of  the  satellites  do  not 
harmonize  with  each  other ;  and  has  thence  inferred  that  the 
same  discordance  should  be  expected  between  the  masses  of  Nep- 
tune as  deduced  from  the  perturbations  of  Uranus  and  from  the 
satellite  observations.  It  is  an  interesting  question,  and  one 
which  still  remains  open,  whether  the  discrepancies  between  the 
two  computations  of  the  mass  of  Uranus  might  not  be  reconciled 
by  a  proper  investigation  of  the  influence  of  Neptune  upon  Sat- 
urn. This  is  one  of  the  most  important  questions,  connected 
with  Neptune,  which  remain  undecided,  and  it  is  earnestly  to  be 
hoped  that  some  one  of  the  three  illustrious  geometers  who 
have  labored  so  faithfully  upon  the  perturbations  of  Uranus  by 
Neptune  may  now  investigate  the  Saturn-perturbations  produced 
by  the  new  planet. 

The  only  other  point  of  Mr.  Le  Verrier's  argument  to  which  I 
will  allude  is  that  in  which  he  says,2  —  "  The  orbit  calculated  by 
Mr.  Walker,  from  a  position  in  1795,  and  the  small  arc  observed 
since  the  discovery,  can  very  well  be  erroneous  by  many  de- 
grees, either  in  1887  or  in  1757,  and  if  I  have  admitted  the 
positions  which  it  has  given  for  these  epochs,  it  is  solely  by  cour- 
tesy, and  because  it  presents  for  me  no  inconvenience."  Of  this 
I  may  be  permitted  to  say,  that  Mr.  Walker's  laborious  and  ac- 
curate investigations  have  given  us  the  orbit  of  Neptune  to  a 
very  high  degree  of  precision,  and  deserve  the  gratitude  and  ad- 
miration of  astronomers,  —  not  such  an  imputation  as  this.  It 
would  be  contrary  to  all  probability  should  the  place  given  by 
Mr.  Walker's  orbit  for  those  years  be  false  by  two  minutes.* 

*  Walker's  orbit  represents  the  course  of  Neptune  as  well  as  can  be  possibly 
desired  from  1795  to  1848,  an  interval  of  53  years.  The  error  in  1887  or  1757 
would,  according  to  the  doctrine  of  chances,  be  to  that  in  either  of  the  years  above 
named  in  the  ratio  652  :  27*  =  5".8  :  1".0,  and  the  resulting  error,  therefore,  less 
than  six  seconds. 

1  Comptes  Rendus,  XXVII.  p.  278.  z  Ibid.,  p.  327. 


THE  DISCOVERY   OF  NEPTUNE.  55 

We  have  seen  that  it  represented  the  observations  so  perfectly 
during  the  opposition  of  1848,  as  to  need  no  correction  whatso- 
ever. 

The  argument1  of  Sir  John  Herschel  is  mostly  based  upon 
the  circumstance,  that  the  directions  of  the  real  and  of  the  hy- 
pothetical planet  were  nearly  identical  at  the  time  of  Neptune's 
discovery,  and  upon  the  fact  that  the  radius-vectors  were  not 
very  different  at  that  time.  But  surely  it  cannot  be  considered 
as  an  analogy  between  the  two  orbits,  that  the  perihelion  of  one 
was  so  near  the  aphelion  of  the  other. 

Reasoning  like  this  seems,  however,  utterly  inapplicable  to 
researches  of  such  nicety  and  analytical  refinement  as  character- 
ize those  upon  the  perturbations  of  Uranus.  It  would  allow  to 
these  investigations  no  other  merit  than  the  success  with  which 
Neptune's  apparent  place  was  approximately  predicted.  It  is 
an  effort  to  show  that  the  uncertainty  of  the  calculations  was  so 
great,  that  Neptune's  perturbative  influence  may  be  included 
within  their  limits. 

The  debt  of  gratitude  which  astronomy  owes  to  Le  Verrier 
and  to  Adams  may  not  be  thus  diminished.  The  arguments, 
which  tend  to  prove  that  Neptune  is  the  planet  of  their  theory, 
can  only  be  based  upon  the  supposition  of  error  in  that  theory,  a 
supposition  which  I  am  unwilling  to  admit.  Investigations  con- 
ducted with  the  care  and  precision  which  characterized  these 
must  not  be  so  lightly  dealt  with.  The  combined  labors  of  Le 
Yerrier  and  Peirce  have  incontrovertibly  proved,  that,  by  re- 
ducing the  limits  of  error  assumed  for  the  modern  observations 
to  3",  there  can  be  but  two  possible  solutions  of  the  problem 
There  are  two  different  mean  distances  of  least  possible  error,  — 
one  of  which  is  36,  and  the  other  30.  The  one  is  included  with- 
in the  theory  and  limits  of  Le  Verrier,  and  corresponds  with 
Adams's  solution;  the  other  is  the  orbit  of  Neptune. 

This  simple  view  of  the  case  —  a  view  which  it  seems  to  me 
impossible  for  those  not  interested  in  the  matter  to  avoid  taking 

1    Outlines  of  Astronomy,  pp.  511,  516. 


56  HISTORY   OF   THE   DISCOVERY   OF  NEPTUNE. 

—  reconciles  all  the  computations  and  observations,  as  well  as  the 
discords  and  contentions.  It  does  not  detract  in  the  slightest 
degree  from  the  well-earned  fame  of  the  illustrious  geome- 
ters, who  had  arrived  at  a  solution  of  the  problem,  and  I  am 
not  aware  that  it  has  ever  been  opposed  by  mathematical  rea- 
soning. 

CAMBRIDGE,  July,  1849. 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


. 
DEC  27 


2  7  1961 


LD  21  A-50m-8,'61 
(Cl795slO)476B 


General  Library 

University  of  California 

Berkeley 


Caylord  Bros. 

Makers 
Syracuse.  N.  Y, 

PAT.  JAN.  21,  1998 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


